hw1_sol - IEOR 172 Probability and Risk Analysis for...

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IEOR 172: Probability and Risk Analysis for Engineers, Fall 2007 Homework 1 Solution Chapter 1 Question 4 There are 4! possible arrangements. By assigning instruments to Jay, Jack, John and Jim, in that order, we see by the generalized basic principle that there are 2! · 2! = 4 possibilities. Question 6 Each kitten can be identified by a code number i , j , k , l where each of i , j , k , l is any of the numbers from 1 to 7. The number i represents which wife is carrying the kitten; j then represents which of that wife’s 7 sacks contain the kitten; and k represents which of the 7 cats in sack j of wife i is the mother of the kitten; and l represents the number of the kitten of cat k in sack j of wife i . By the generalized principle there are thus 7 · 7 · 7 · 7 = 2401 kittens. Question 10 (a) 8! = 40 , 320 (b) 2 · 7! = 10 , 080 (c) 2 · 4! · 4! = 1152 (d) 5! · 4! = 2 , 880 (e) 4! · 2 4 = 384 Question 15 There are 10 5 ! 12 5 ! possible choices of the 5 men and 5 women. They can then be paired up in 5! ways, so there are 5! 10 5 ! 12 5 ! possible results. Question 21 7! 3!
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hw1_sol - IEOR 172 Probability and Risk Analysis for...

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