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*****In addition to this review, I recommend that you attend all classes, complete and review all homework assignments, and take any steps you consider necessary for yourself to succeed in the course. Evaluate the expression. 1) 3! Answer: 6 2) 11C2 Answer: 55 3) 12C0 Answer: 1 4) 5P4 Answer: 120 5) 8P4 Answer: 1680 5) 4) 3) 2) 1)

6) How many different 4-digit sequences can be formed using the digits 0, 1,...,9 if repetition of digits is allowed? Answer: 10,000

6)

7) A shirt company has 3 designs each of which can be made with short or long sleeves. There are 5 color patterns available. How many different types of shirts are available from this company? Answer: 30

7)

1

8) How many different 8-digit sequences can be formed using the digits 0, 1,...,9 if repetition of digits is allowed? Answer: 100,000,000

8)

9) License plates are made using 2 letters followed by 3 digits. How many plates can be made if repetition of letters and digits is allowed? Answer: 676,000

9)

10) A shirt company has 3 designs each of which can be made with short or long sleeves. There are 6 color patterns available. How many different types of shirts are available from this company? Answer: 36

10)

11) If 4 newborn babies are randomly selected, how many different gender sequences are possible? Answer: 16

11)

12) How many different sequences of 4 digits are possible if the first digit must be 3, 4, or 5 and if the sequence may not end in 000? Repetition of digits is allowed. Answer: 2997

12)

13) A restaurant offers 8 possible appetizers, 9 possible main courses, and 8 possible desserts. How many different meals are possible at this restaurant? (Two meals are considered different unless all three courses are the same). Answer: 576

13)

14) How many different 4-letter radio station call letters can be made if repeats are allowed and the first letter must be K. Answer: 17,576

14)

15) How many different 7-digit phone numbers are possible if the first digit cannot be a 0? Answer: 9,000,000

15)

2

16) How many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetition of digits is not allowed? Answer: 210

16)

17) How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to choose from? Answer: 20,160

17)

18) A musician plans to perform 7 selections. In how many ways can she arrange the musical selections? Answer: 5040

18)

19) A musician plans to perform 4 selections. In how many ways can she arrange the musical selections? Answer: 24

19)

20) There are 9 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible? Answer: 504

20)

21) In a game of musical chairs, 10 children will sit in 9 chairs arranged in a row (one child will not find a chair). In how many ways can 9 of the children find seats? Answer: 3,628,800

21)

22) In how many ways can 2 letters be chosen from the set {A, B, C, D, E, F} if order is important and no repeats are allowed? Answer: 30

22)

23) There are 12 members on a board of directors. If they must form a subcommittee of 4 members, how many different subcommittees are possible? Answer: 495

23)

3

24) There are 13 members on a board of directors. If they must form a subcommittee of 6 members, how many different subcommittees are possible? Answer: 1716

24)

25) The library is to be given 5 books as a gift. The books will be selected from a list of 27 titles. If each book selected must have a different title, how many possible selections are there? Answer: 80,730 26) In a certain lottery, 4 numbers between 1 and 13 inclusive are drawn. These are the winning numbers. How many different selections are possible? Assume that the order in which the numbers are drawn is not...