Alice Bob Celia Don are members of a club.

1. Bob Celia Don Alice Alice Celia Bob Don Celia Alice Bob Don Don Alice Bob Celia Alice Bob Celia Don are members of a club. In how many ways can they select a president and vice president ? 4 x 3 = 12

2. Alice 1.) 2.) Bob Celia 4.) Don 5.) 6.) 3.) AliceBob Celia Don are members of a club. In how many ways can they select a 2 person committee? Bob Celia Don Alice Celia Don Alice Bob Don Alice Bob Celia

3. Bob Celia Alice Celia Bob Alice Celia Bob Celia Alice Alice Bob Celia Bob Alice AliceBob Celia are running for pres., vice pres., and secretary There are 6 different ways of arranging 3 people in order. The number of possible outcomes = 3 x 2 x 1 = 6

4. Alice Bob Celia Don Edna are members of a club. There are 5 ways to select a pres. For each of the 5 ways to select a pres., there are 4 ways to select a vice pres. For each of the 20 ways to select pres. and vice pres., there are 3 ways to select a secretary. 5 x 4 x 3 = 60 In how many ways can they select a pres., vice pres., and secretary?

5. In how many ways can they select a 3 person committee? AliceBob Celia Don Edna There are 60 branches on this tree - 60 ways to select 3 people in order But each 3 person committee is repeated 6 times on this list of 60.

6. In how many ways can they select a 3 person committee? AliceBob Celia Don Edna This one committee appears 6 times

7. In how many ways can they select a 3 person committee? AliceBob Celia Don Edna And this committee appears 6 times

8. AliceBob 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 repetitionsof 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