Chapter 1: Permutations
1. In how many ways can three different awards be distributed among 20 students in the following situations? a. No student may receive more than one award.
b. There is no limit on the number of awards won by one student. Answer: a) 6840 b)8000
2. Consider the word BASKETBALL:
a. How many permutations are there?
b. How many permutations begin with the letter K?
c. How many permutations have the two L’s together?
Answer: a) 453 600 b) 45 360 c) 90 720
3. How many 3-digit numbers can be formed using only the digits 1 to 7, if the number 2 must be included? (Repetitions are allowed.)
4. How many arrangements of the word ALGORITHM bein with a vowel and end with a consonant?
Answer: 90 720
5. Prove: [pic]
Chapter 2: Combinations
6. How many bridge hands (13 cards) contain five clubs, two hearts, three diamonds, and three spades? Leave answer in factorial form. Answer: [pic]
7. In how many ways can 12 prizes be awarded evenly among four people? Answer: 369 600
8. From a deck of 52 cards, how many different four-card hands could be dealt which include one card from each suit?
Answer: 28 561
9. Find the number of divisors of 540 other than 1.
10. The swise embassy in Ottawa has 65 employees. Of these workers, 47 speak German, 35 speak Italian, and 20 speak both German and Italian. How many embassy employees speak neither German nor Italian? Illustrate the situation with a Venn diagram.
11. Solve for [pic]:
Chapter 3: The Binomial Theorem
12. If [pic], find n.
13. In the expansion of [pic], find the following:
a. The general term
b. The term containing [pic]
c. The constant term.
Answer: a) [pic] b) [pic] c) –2268 14. In the expansion of [pic], find the term containing x.
Chapter 6 (New Text): Introduction to Probability
15. An integer from 1 to 50 inclusive is chosen at random. What is the probability that the integer is: a. Odd?
b. Not a perfect square?
Answer: a) 0.5 b) 43/50
16. In a track meet, five entrants of equal ability are competing. What is the probability that: a. The finish wil be in the descending order of the entrants’ ages? b. Sandy will be first?
Answer: a) 1/120 b) 1/5
17. Hans has 12 good friends, five of them male and seven of them female. He decides to have a dinner party but can invite only seven because his dining room table will seat only 8 people. He decides to invite his guests by lot (picking names out of a hat.) What is the probability that a. There will be four males and four females at the party? b. Rivka will be among those invited?
Answer: a) 0.44 b) 0.58
18. A is the event of rolling a prime number with a die.
B is the event of rolling a perfect square with a die.
C is the event of rolling an even number with a die.
Answer: a) 5/6 b) 2/3
19. A die is rolled twice. What is the probability that the sum of the rolls is less than 4 given that one of the rolls is a 1?
20. What is the probability that there are at least two people with the same birthday in a class of 40 students?
21. A confident and boastful coach claims that on the next league game the odds of his team winning are 3:1; the odds against losing are 5:1; and the odds against a tie are 7:1. Can these odds be right? Explain.
22. Andrea and Ling are evenly matched tennis players. However, each time Ling loses a game his probability of winning the next game is decreased by 1/5. But when he wins, his probability of...
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