Combinations WS Algebra 2 Name: Unit 11 Date: 1. Find the number of ways of making each choice. a. Selecting three days out of a week b. Selecting three days out of a week if exactly two of them must be weekdays c. Selecting a 4-member committee from a 20-member club d. Selecting a 4-member committee from a 20-member club if the president of the club must be on the committee e. Selecting a 4-member committee from a 20-member club if the president of the club cannot be on the committee but the treasurer must be on the committee f. Selecting a 4-member committee from a 20-member club if there are 12 women and 8 men in the club and the committee must include 2 men and 2 women 2. There are 8 fourth graders, 14 fifth graders, and 12 sixth graders in a Girl Scout troop. Mrs. Sullivan, the troop leader, needs six girls to serve on the troop’s camping committee. To make the selection fair, she lets the girls draw names out of a hat to fill the six places on the committee. a. How many different committees are possible? b. What is the probability that Lisa Brownell, one of the sixth-grade scouts, will be on the committee? c. What is the probability that Lisa and her best friend, Naomi Weiss, will both be on the committee? d. What is the probability that all the committee members will be fifth graders? e. What is the probability that the committee will be made up of 2 fourth graders, 3 fifth graders, and 1 sixth grader? 3. Nine people apply to go on a medicine-related field trip, but there is only room in the van for seven of them. In how many different ways could the group of seven making the trip be chosen? 4. A donut store sells 30 varieties of donuts. Suppose one of the stores decides to make sample boxes with twelve different donuts in each box. How many different sample boxes could be made? 5. A teacher has a collection of 24 true-false questions and wishes to choose 10 of them for a quiz. How many quizzes can be made if the order of the questions is considered a. important? b. unimportant? 6. A pizzeria offers 13 different toppings. Find the number of different kinds of pizza they could make using a. Four toppings b. Seven toppings 7. Nine people apply for 3 job positions. In how many ways can the 3 positions be filled if the positions are a. all different? b. all the same? 8. A standard deck of playing cards has 52 cards. a. How many different 13-card bridge hands could be formed? b. How many different 5-card poker hands could be formed? 9. Of the 12 players on a high school basketball team, the coach must choose 5 players to be in the starting line-up. In how many ways can the coach select the starting line-up if the playing positions are a. considered? b. not considered? 10. Three couples go to the movies and sit together in a row of six seats. In how many ways can these people arrange themselves if each couple sits together?