Answer Questions #2-7, 9-11, and 13-14. Show work.

2) Your closet contains 10 different styles of shoes. In how many ways can you pick out five different styles of shoes for the school week if you don’t care which day of the week you wear each style?

3) Your closet contains 10 different styles of shoes. In how many ways can you pick out five different styles of shoes for the school week if you do care which day of the week you wear each style?

4) You are drawing a rainbow using five different colored crayons from your box of 24 colors. In how many ways can you draw a rainbow if the first color you pick will be the top layer and so on?

5) You are drawing a rainbow using five different colored crayons from your box of 24 colors. In how many ways can you pick the five colors for your rainbow?

6) How many 5 card poker hands can be dealt from a standard 52 card deck?

7) Suppose the majority party in a foreign country must select a prime minister and secretary of state from an eligible group of 36 party members. In how many ways can this be done?

9) There are 7 women and 5 men in a department. Four people are needed for a committee. a) In how many ways can a committee of 4 people be selected? b) In how many ways can this committee be selected if there must be exactly 2 men and 2 women on the committee? c) In how many ways can this committee be selected if there must be at least 2 women on the committee?

10) A company has 8 cars and 11 trucks. The state inspector will select 3 cars and 4 trucks to be tested for safety inspections? In how many ways can this be done?

11) In a train yard there are 4 tanker cars, 12 boxcars, and 7 flatcars available for a train. In how many ways can a train be made up consisting of 2 tanker cars, 5 boxcars, and 3 flatcars?

13) In how many ways can a jury of 12 people be selected from a pool of 12 men and 10 women?

14) In how many ways can a jury of 6 men and 6 women be selected from a pool of 12 men and 10 women?

 

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