Practice and Problem-Solving Exercises

A Practice

See Problem 1.

11. Telephones A seven-digit telephone number can begin with any digit except 0 or 1. There are no restrictions on digits after the first digit.
    1. How many possible choices are there for the first digit? For each digit after the first digit?
    2. How many different seven-digit telephone numbers are possible?
12. Use the diagram and the Multiplication Counting Principle to find each of the following:

    

    1. the number of routes from A to C
    2. the number of routes from A to D

    See Problem 2.

13. Sports In an ice-skating competition, the order in which competitors skate is determined by a drawing. Suppose there are 10 skaters in the finals. How many different orders are possible for the final program?
14. Photography Suppose you are lining up with 4 cousins for a photo. How many different arrangements are possible?

See Problem 3.

Find the value of each expression.

15.   8 P 4 sub 8 , cap p sub 4
16.   9 P 3 sub 9 , cap p sub 3
17.   7 P 6 sub 7 , cap p sub 6
18.   8 P 5 sub 8 , cap p sub 5
19.   7 P 2 sub 7 , cap p sub 2
20.   5 P 5 sub 5 , cap p sub 5
21.   6 P 1 sub 6 , cap p sub 1
22.   11 P 0 sub 11 , cap p sub 0
23.   10 P 2 sub 10 , cap p sub 2
24.   12 P 9 sub 12 , cap p sub 9
25. Reading You have 10 books on your bookshelf. In how many orders can you read 4 of the books on a summer vacation?
26. Student Government A student council has 24 members. The council is selecting a 3-person committee to plan a car wash. Each person on the committee will have one task: one person will find a location, another person will organize publicity, and the third person will schedule volunteers. In how many different ways can 3 students be chosen and given a task?

See Problem 4.

Find the value of each expression.

27.   6 C 6 sub 6 , cap c sub 6
28.   5 C 4 sub 5 , cap c sub 4
29.   9 C 1 sub 9 , cap c sub 1
30.   7 C 2 sub 7 , cap c sub 2
31.   8 C 5 sub 8 , cap c sub 5
32.   3 C 0 sub 3 , cap c sub 0
33.   8 C 6 sub 8 , cap c sub 6
34.   7 C 5 sub 7 , cap c sub 5
35.   10 C 9 sub 10 , cap c sub 9
36.   15 C 4 sub 15 , cap c sub 4
37. Law For some civil cases, at least 9 of 12 jurors must agree on a verdict. How many combinations of 9 jurors are possible on a 12-person jury?
38. Gift Certificates For your birthday you received a gift certificate from a music store for 3 CDs. There are 8 CDs you would like to have. How many different groups of 3 CDs can you select from the 8 you want?
39. Quilting There are 30 fabrics available at a quilt store. How many different groups of 5 fabrics can you choose for a quilt?

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