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

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

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

5. 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 are 4 ways to select a vice pres. 5 x 4 x 3 = 60 For each of the 20 ways to select pres. and vice pres., there are 3 ways to select a secretary.

6. Alice Bob Celia Don Edna In how many ways can they select a 3 person committee? 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.

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

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

9. 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