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Example: Ways to pick officers | Probability and combinatorics | Precalculus | Khan Academy

Video vocabulary

club

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US / klʌb /

UK / klʌb /

A1
  • noun
  • Group of people who share an interest, as in sport
  • Place where people go to listen to music and dance
  • Long stick used for hitting things, as in golf
  • verb
  • To be grouped with others
  • To hit hard with a thick and heavy stick, weapon

someone

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US / ˈsʌmwʌn /

UK / ˈsʌmˌwʌn, -wən /

A1
  • pronoun
  • Person who is not known or named

many

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US / 'menɪ /

UK / ˈmɛni /

A1
  • determiner
  • Used to refer a large number of things

matter

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US / 'mætə(r) /

UK / ˈmætɚ /

A1
  • noun
  • Material all things are made of that fills space
  • Problem or reason for concern
  • verb
  • To be of great importance; to count

actually

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US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

either

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US / ˈaɪðə(r) /

UK / ˈiðɚ, ˈaɪðɚ /

A1
  • adjecitve
  • One of two (used when there is a choice of two)
  • adverb
  • (After negative statements) likewise, in addition
  • conjunction
  • Used as the first of two connected things
  • determiner
  • Used as the first of two connected things
  • pronoun
  • The one or the other

position

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US / pəˈzɪʃn /

UK / pəˈzɪʃən /

A1
  • noun
  • Person's opinion or attitude about something
  • Specific location where someone or something is
  • Where you play or your role on a sports team
  • Person's job or status level
  • Set of conditions affecting what you can (not) do
  • verb
  • To put in a particular location or direction

plus

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US / plʌs /

UK / plʌs /

A2
  • noun
  • A benefit or advantage
  • preposition
  • In addition; add
  • In addition to; Indicates a number above
  • Having a value greater than zero

slot

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US / slɒt /

UK / slɑ:t /

B1
  • noun
  • A long narrow opening to put a coin, etc. in
  • verb
  • To put something in a small narrow opening

about

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US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

different

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US / ˈdɪfrənt /

UK / ˈdɪfrənt /

A1
  • adjecitve
  • Not of the same kind; unlike other things

people

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US / 'pi:pl /

UK / ˈpipəl /

A1
  • noun
  • Persons sharing culture, country, background, etc.
  • Men, Women, Children

that

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US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

right

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US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

she

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US / ʃɪ /

UK / ʃi /

A1
  • pronoun
  • Female person or animal mentioned before
  • (Refers to female person mentioned before)

then

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US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

first

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US / fɜ:st /

UK / fɚst /

A1
  • adjecitve
  • 1st; Coming before all others in time or place
  • noun
  • Something that has not happened before
  • Position of the winner of a competition

get

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US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

president

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US / ˈprezɪdənt /

UK / ˈprɛzɪdənt,-ˌdɛnt /

A2
  • noun
  • Person in charge of a country, or organization

for

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US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

time

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US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

board

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US / bɔ:d /

UK / bɔrd, bord /

A1
  • noun
  • Surface for posting or showing information
  • Group of persons who direct an organization
  • Long piece of material used for riding the waves
  • Long thin piece of wood, used for building; plank
  • verb
  • To enter a ship, plane, or other vehicle
  • To cover with long wooden strips of wood
  • To pay money to live in someone's house; lodge

just

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US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

vice

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US / ˌvaɪs /

UK / ˌvaɪ.sə /

B2
  • adverb
  • used to say that what you have just said is also true in the opposite order

those

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US / ðəʊz /

UK / ðoz /

A1
  • determiner
  • The people or things we are talking about
  • pronoun
  • The objects far from the speaker

well

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US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears

eight

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US / eɪt /

UK / et /

A1
  • number
  • 8

could

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US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

choice

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US / tʃɔɪs /

UK / tʃɔɪs /

A1
  • adjecitve
  • Of good quality or taste; desirable
  • noun
  • Decision between two or more possibilities

see

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US / si: /

UK / si /

A1
  • verb
  • To go on a date with someone
  • To predict whether something is, or will be true
  • To understand what someone says
  • To use your eyes to look at something
  • To visit a place often for sightseeing or pleasure
  • To visit or meet with someone
  • To find out by waiting or looking
  • To watch (a game, movie or TV show)

have

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US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

last

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US / lɑ:st /

UK / læst /

A1
  • adjecitve
  • Most recent; the latest
  • The one before
  • adverb
  • Final; with nothing following; after all others
  • Most recent; the latest
  • determiner
  • The one at the end
  • verb
  • To remain or continue for a certain period of time

they

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US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

appoint

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US / ə'pɔɪnt /

UK / əˈpɔɪnt /

A2
  • verb
  • To officially choose a person for a job, position

way

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US / weɪ /

UK / we /

A1
  • adverb
  • Used to emphasize the amount of something
  • noun
  • Particular aspect of something being thought about
  • One of various choices that could be made
  • Particular existing condition or state
  • (Often long) distance or length of time
  • How something is done
  • Route to go to a place
  • Small street
  • Usual behavior, emotions or habits of someone

hold

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US / həʊld /

UK / hold /

A1
  • noun
  • Section of a ship or plane used for storing things
  • Influence or power held over someone
  • Place of support for hands or feet when climbing
  • verb
  • To agree to keep something for someone
  • To have the capacity to support/contain something
  • To control an area and protect it from attack
  • To not allow someone to leave a place
  • To cause an event to happen at a place or time
  • To use hands or arms to carry or keep something
  • To have a specific quality or property
  • To keep an image, belief or feeling in your mind
  • To have or own something
  • To wait before being able to talk on the phone
  • To limit the movement of someone in a sport

possible

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US / ˈpɒsəbl /

UK / ˈpɑsəbəl /

A1
  • adjecitve
  • Being able or appropriate for a task or purpose
  • Having a chance of happening, or being true

take

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US / teɪk /

UK / tek /

A1
  • noun
  • Filming of a single scene for TV or the movies
  • verb
  • To accept something that is offered
  • To use a method of traveling, e.g. a bus or train
  • To use a camera to make (a photo)
  • To pick up something and go away with it
  • To study a subject in school
  • To attempt to pass (an exam)
  • To require a certain amount of time, money, space

all

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US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

officer

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US / ˈɒfɪsə(r) /

UK / ˈɔ:fɪsə(r) /

B1
  • noun
  • Person of high position in an organization
  • Person of high position in the military

from

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US / frəm /

UK / frʌm, frɑm,frəm /

A1
  • preposition
  • Starting at a particular place, time or level

out

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US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

and

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US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

office

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US / ˈɒfɪs /

UK / ˈɔ:fɪs /

A1
  • noun
  • Room or building used for business
  • Important job position, often in a government

leave

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US / li:v /

UK / liv /

A1
  • noun
  • Permission to do something
  • Vacation time; time off work
  • verb
  • To go away from; depart
  • To gift property to someone after you die
  • To allow something to continue happening
  • To let something remain unused or available
  • To let something or someone remain somewhere

nine

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US / naɪn /

UK / naɪn /

A1
  • number
  • 9

possibility

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US / ˌpɒsə'bɪlətɪ /

UK / ˌpɑsəˈbɪlɪti /

A2
  • noun
  • Something with a chance of happening or being true

only

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US / ˈəunli /

UK / ˈonli /

A1
  • adverb
  • Just one; just that amount or thing; not more than
  • Not very important or serious
  • Just that type of thing, person
  • Short time ago; not before a certain time
  • conjunction
  • Except; but

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

any

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US / 'enɪ /

UK / ˈɛni /

A1
  • adjecitve
  • One, or some, no matter which
  • pronoun
  • One (thing) of many; some

secretary

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US / 'sekrətrɪ /

UK / ˈsɛkrɪˌtɛri /

A1
  • noun
  • Office worker who makes appointments, etc.
  • Official in charge of a governmental department

think

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US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something

now

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US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

can

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US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

seven

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US / ˈsevn /

UK / ˈsɛvən /

A1
  • number
  • Number 7

yet

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US / jet /

UK / jɛt /

A1
  • adverb
  • At a later time (used after ‘not’)
  • (Used to emphasize that thing is, will be greater)
  • Eventually; at a future time
  • Until now; up to the present
  • conjunction
  • Adding to what has been said, often as a contrast

want

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US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

but

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US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

pick

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US / pɪk /

UK / pɪk /

A1
  • noun
  • Sharp tool used for breaking the ground
  • Item selected from a group of choices
  • verb
  • To take fruit or vegetables from a plant or tree
  • To decide on a thing from various choices; select
  • To remove (flower, etc.) with your fingers

would

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US / wʊd /

UK / wʊd /

A1
  • other
  • Used to indicate something imagined
  • Used to ask or request something politely
  • Verb used to indicate possibility, request etc.
  • Used to indicate a preference
  • Used to indicate a reaction
  • Indicates something that occurred repeatedly
  • Used to indicate willingness or ability to do

not

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US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

also

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US / 'ɔ:lsəʊ /

UK / ˈɔlso /

A1
  • adverb
  • In addition; too; in a similar way

how

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US / haʊ /

UK / haʊ /

A1
  • adjecitve
  • To what degree? in what amount?
  • adverb
  • (Used to explain the way to do something)
  • exclamation
  • For what purpose or reason?
  • (Used to ask someone or something's condition)

kind

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US / kaɪnd /

UK / kaɪnd /

A1
  • adjecitve
  • In a caring and helpful manner
  • friendly and considerate
  • noun
  • One type of thing

you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

other

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US / 'ʌðə(r) /

UK / ˈʌðər /

A1
  • adjecitve
  • A thing different from that mentioned
  • determiner
  • (Something) else; not the first (one)
  • pronoun
  • Being the one and only thing of that category

one

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US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

than

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US / ðən /

UK / ðən /

A1
  • conjunction
  • Used to compare two things that are not equal

candidate

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US / ˈkændɪdət /

UK / ˈkændɪˌdet, -dɪt /

B1
  • noun
  • Politician who is running for public office

run

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US / rʌn /

UK / rʌn /

A1
  • noun
  • Journey between two places made by ship or car
  • Series of similar things or successes and failures
  • Act of running; exercise of running
  • verb
  • To depart or travel according to a schedule
  • To cause an animal to move in a certain direction
  • (Of an engine) to be operating
  • To start or use a computer program
  • To flow in a certain direction, like a liquid
  • To manage or operate a business
  • To operate or drive something
  • (Of a road) to go from one place to another
  • To move your legs faster than walking

three

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US / θri: /

UK / θri /

A1
  • number
  • Number 3

this

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US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

valid

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US / 'vælɪd /

UK / ˈvælɪd /

A2
  • adjecitve
  • Being in effect or in force, often legally
  • Reasonable; based on sound assumptions
  • Working correctly; producing results

let

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US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

person

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US / 'pɜ:sn /

UK / 'pɜ:rsn /

A1
  • noun
  • Man, woman or child

the

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US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family
  • Subtitles section
  • A club of nine people wants to choose a board of three officers: a President, a Vice President, and a Secretary.
  • How many ways are there to choose the board from the nine people?
  • Now, we're going to assume that one person can't hold more than one office.
  • That if I'm picked for President, then I'm no longer a valid person for Vice President or Secretary.
  • So let's just think about the three different positions.
  • So you have the President, you have the Vice President, VP, and then you have the Secretary.
  • Now, let's say that we go for the President first. It actually doesn't matter.
  • Let's say we were picking the President slot first and we haven't appointed any other slots yet.
  • How many possibilities are there for President?
  • Well, the club has nine people, so there's nine possibilities for President.
  • There's going to be nine possibilities for President.
  • Now, we're going to pick one of those nine.
  • We're going to kind of take them out of the running for the other two offices.
  • Right?
  • Because someone's going to be President, so one of the nine is going to be President.
  • There's nine possibilities, but one of the nine is going to be President.
  • So you take that person aside.
  • He or she is now the President.
  • How many people are left to be Vice President?
  • Well, now there's only eight possible candidates for Vice President?
  • Eight possibilities.
  • Now he or she also goes aside.
  • Now how many people are left for Secretary?
  • Well, now there's only seven possibilities for Secretary.
  • So if you want to think about all of the different ways there are to choose a board from the nine people, there's the 9 for President times the 8 for Vice President times the 7 for Secretary.
  • You didn't have to do it this way.
  • It could've been-- you could've picked Secretary first. Then there would've been nine choices.
  • And then you could've picked Vice President, and there would've still been eight choices.
  • And then you could've picked President last, and there would've only been seven choices.
  • But either way you would've got 9 times 8 times 7.
  • And that is, let's see, 9 times 8 is 72 times 7 is-- 2 times 7 is 14, 7 times 7 is 49 plus 1 is 50.
  • So 504 possible ways to pick your board out of a club of only nine people.