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Question: 14 how many ways are there to select a firstprize...

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14. How many ways are there to select a first-prize winner, a second-prize winner, and a third-prize from 100 different people who have entered a contest? AP(100, 3) B. C(100, 3) C. 1001-3! D. 31- 6 15. The following 8 x 24 grid is divided into squares that are 1 unit by 1 unit. The shortest possible path on this grid from A to B is 32 units long. One such path is shown in the figure. Let X be the set of all 32-unit-long paths from Ato B. what is lx1, the number of 32-unit-long paths from A to B? A. C(24, 8) B. C(32, 8) -С. P(24, 8) D. P(32, 8) 16. Suppose that 100 lottery tickets are given out in sequence to the first 100 guests to arrive at a party. Of these 100 tickets, only 12 are winning tickets. The generalized pigeonhole principle guarantees that there must be a streak of at least m losing tickets in a row. (假設有100張彩票按順序發放給前100位 客人參加派對.在這100張門票中,只有12張是中獎門票.廣義的鴿籠原則保證了遠續未申 獎的門票數量為.)What is m? A. 10 B.9 C8 D.7 17. How many positive integers less than 100,000 have the sum of their digits equal to 172 A. 4336 B. 4335 C. 5985 D. 5986 18. What is the minimum um number of students required in a discrete mathematics class to be sure that at students re least six will receive the same grade, if there are five po A, 6 B, 12 С. 25,1 D. 26 ssible grades, A, B, C, D, and F? 19. How many ways are there to rearrange the letters in FUNCTION? A. C(8, 2) B. C(8, 8) C. P(8, 2) D. P(8, 8) ferent classes. No two classes can meet at the same time in the same 12 different time slots at which classes can occur. What is the minimum 20. A small college offers 250 dif room, of course. There are ti number of classrooms needed to accommodate all A. 19 B. 20 C. 21 D. 22 the classes?
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