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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 Fall '07
 righter
 Trigraph, Jack, Jay, Jim, TwoFace

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