Practice and Problem-Solving Exercises

A Practice

See Problem 1.

9. You have five shirts and four pairs of pants. How many different ways can you arrange your shirts and pants into outfits?
10. To create an entry code, you need to first choose a letter and then, three single-digit numbers. How many different entry codes can you create?

11. The prom committee has four sites available for the banquet and three sites for the dance. How many arrangements are possible for the banquet and dance?

    See Problem 2.

    Evaluate each expression.

12. 5!
13. 10!
14. 13!
15. 5!3!
16. 12 ! 6 ! fraction 12 factorial , over 6 factorial end fraction
17. 5(4!)
18. 10 ! 7 ! 3 ! fraction 10 factorial , over 7 factorial 3 factorial end fraction
19. 15 ! 10 ! 5 ! fraction 15 factorial , over 10 factorial 5 factorial end fraction
20. Automobiles You should rotate tires on a car at regular intervals.
    1. In how many ways can four tires be arranged on a car?
    2. If a spare tire is included, how many arrangements are possible?

See Problem 3.

Evaluate each expression

21.   8 P 1 sub 8 , cap p sub 1
22.   8 P 2 sub 8 , cap p sub 2
23.   8 P 3 sub 8 , cap p sub 3
24.   8 P 4 sub 8 , cap p sub 4
25.   3 P 2 sub 3 , cap p sub 2
26.   5 P 4 sub 5 , cap p sub 4
27.   9 P 6 sub 9 , cap p sub 6
28.   7 P 4 sub 7 , cap p sub 4
29. Scheduling Fifteen students ask to visit a college admissions counselor. Each scheduled visit includes one student. In how many ways can ten time slots be assigned?

See Problem 4.

Evaluate each expression.

30.   6 C 2 sub 6 , cap c sub 2
31.   8 C 5 sub 8 , cap c sub 5
32.   4 C 4 sub 4 , cap c sub 4
33.   4 C 3 sub 4 , cap c sub 3
34.   7 C 3 sub 7 , cap c sub 3
35. 3 (   5 C 4 ) 3 open , sub 5 , cap c sub 4 , close
36.   6 C 2 +   6 C 3 sub 6 , cap c sub 2 , plus , sub 6 , cap c sub 3
37.   7 C 4   9 C 4 fraction sub 7 , cap c sub 4 , over sub 9 , cap c sub 4 end fraction
38. Awards There are eight swimmers in a competition where the top three swimmers advance. In how many ways can three swimmers advance?

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