need help with the numbers 2, 4, 6, 12, 16 today on a doc document please by 9pm just the answers.

1. Compute each of the following. 8. How many different eight-card hands with five red cards (a) 7C7 (b) 7C4 (C) 16 Cs and three black cards can be dealt from a deck of 52 cards? 2. Compute each of the following. 9. (a) Find the number of subsets of each possible size for (a) . Ca-1 (b) " Cu-2 (c) "+1 Co-1 a set containing four elements. 3. Show that , Cr = , Ca-r. (b) Find the number of subsets of each possible size for 4. In how many ways can a committee of three faculty mem- a set containing n elements. bers and two students be selected from seven faculty For Exercises 10 through 13, suppose that an urn contains 15 members and eight students? balls, of which eight are red and seven are black. 5. In how many ways can a six-card hand be dealt from a 10. In how many ways can five balls be chosen so that deck of 52 cards? (a) all five are red? 6. At a certain college, the housing office has decided to ap- point, for each floor, one male and one female residential (b) all five are black? advisor. How many different pairs of advisors can be se- 11. In how many ways can five balls be chosen so that lected for a seven-story building from 12 male candidates (@) two are red and three are black? and 15 female candidates? (b) three are red and two are black? 7. A microcomputer manufacturer who is designing an ad- vertising campaign is considering six magazines, three 12. In how many ways can five balls be chosen so that at most newspapers, two television stations, and four radio sta- three are black? tions. In how many ways can six advertisements be run if 13. In how many ways can five balls be chosen so that at least (a) all six are to be in magazines? two are red? (b) two are to be in magazines, two are to be in newspa- 14. Give a model in terms of combinations to count the num- pers, one is to be on television, and one is to be on ber of strings of length 6 in (0, 1]" that have exactly four radio? ones. 100 Chapter 3 Counting 15. Give a model in terms of combinations to count the num- (a) record sequences are possible? ber of ways to arrange three of seven people in order from (b) sequences contain exactly one six? youngest to oldest. (c) sequences contain exactly four twos, assuming n 2 16. A committee of six people with one person designated as 47 chair of the committee is to be chosen. How many differ- ent committees of this type can be chosen from a group of 25. How many ways can you choose three of seven fiction 10 people? books and two of six nonfiction books to take with you on your vacation? 17. A gift certificate at a local bookstore allows the recipient to choose six books from the combined list of ten best- 26. For the driving part of your vacation you will take 6 of the selling fiction books and ten bestselling nonfiction books. 35 rock cassettes in your collection, 3 of the 22 classical In how many different ways can the selection of six books cassettes, and 1 of the 8 comedy cassettes. In how many