problems09-sol - MATH S-104 Lecture 9 In-class Problem...

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MATH S-104 Lecture 9 In-class Problem Solutions July 21, 2009 Problem 1 * : a) How many possibilities are there for the win, place and show (first, second and third) positions in a horse race with 12 horses if all orders of finish are possible? P ( 12 , 3 ) = 12! 9! = 12 11 10 = 1320 . b) How many di ff erent sets of three horses can win a place on the podium (that is, first, second or third place)? For this one, we don’t care about the order of the horses. C ( 12 , 3 ) = 12! 3!9! = 12 11 10 3! = 220. c) How many possible results are there for the entire field? There are P ( 12 , 12 ) = 12! = 479 , 001 , 600 ways to order the 12 horses. d) How many possible results are there where the favorite wins a place on the podium? There are 11! possibilities for each of the possible finishes, so there are 3 11! = 11 , 9750 , 400 possibilities. e) If only the first six horses go on to the next race, how many possible sets of horses go on to the next race? C ( 12 , 6 ) = 12! 6!6! = 12 11 10 9 8 7 6! = 924. Problem 2 : b) How many distinguishable orderings of the letters of HULLABALOO begin with U and end with L ?
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