Odds and New Text
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.) Answer: 127
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. Answer: 23
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. Answer: 3
11. Solve for [pic]: [pic] Answer: 8
Chapter 3: The Binomial Theorem
12. If [pic], find n. Answer: 9
13. In the expansion of [pic], find the following: a. The general term b. The term containing
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.) Answer: 127
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. Answer: 23
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. Answer: 3
11. Solve for [pic]: [pic] Answer: 8
Chapter 3: The Binomial Theorem
12. If [pic], find n. Answer: 9
13. In the expansion of [pic], find the following: a. The general term b. The term containing