Alice Bob Celia Don are members of a club.

Alice

Bob

Celia

Don

BobCeliaDon

Alice

Alice

Alice

Celia

Celia

Don

DonBob

Bob

In how many ways can they selecta president and vice president ?

4 x 3 = 12

Alice Bob Celia Don are members of a club.

Alice

Bob

Celia

Don

BobCeliaDon

Alice

Alice

Alice

Celia

Celia

Don

DonBob

Bob

In how many ways can they selecta 2 person committee?

1.)

2.)

3.)

4.)

5.)

6.)

Alice Bob Celia are running for pres., vice pres., and secretary

Bob CeliaAlice

Alice

AliceAlice

Alice

Bob

Bob

Bob

Celia

CeliaCelia

Celia

Bob

The number of possible outcomes = 3 x 2 x 1 = 6

There are 6different waysof arranging3 people inorder.

Alice Bob Celia Don Edna are members of a club.

In how many ways can they select a pres., vice pres., and secretary?

There are 5 ways to select a pres.

For each of the 5 ways to select a pres., there are4 ways to select a vice pres.

5 x 4 x 3 = 60

For each of the 20ways to select pres.and vice pres., there are 3 ways toselect a secretary.

Alice Bob Celia Don Edna

In how many ways can they select a3 person committee?

There are 60 branches on this tree - 60 ways to select 3 people in order

But each 3 person committeeis repeated 6 times on thislist of 60.

Alice Bob Celia Don Edna

In how many ways can they select a3 person committee?

This one committee appears 6 times

Alice Bob Celia Don Edna

In how many ways can they select a3 person committee?

And this committee appears 6 times

Alice Bob Celia Don Edna are members of a club.

The number of ways of selecting

a pres., vice pres., and secretary = 5 x 4 x 3

the number of repetitions of each

3 person committee = 3 x 2 x 1

The number of 3 person committees = 5 x 4 x 3 = 10 3 x 2 x 1