3/27/13
probability  Counting Couples  Mathematics
math.stackexchange.com/questions/336896/countingcouples
1/4
Counting Couples
A group of
men and
women randomly sit in a single row at a theater. If a man and woman
are seated next to each other, they form a "couple." "Couples" can overlap, which means one
person can be a member of two "couples."
m
w
Question: What is the expected number of couples?
Comment: I have a hard time with word problems that deal with "expectations".
(probability) (discretemathematics)
edited
Mar 21 at 14:53
julien
15.2k
1
8
36
asked Mar 21 at 14:17
Sol Bethany Reaves
13
3
–
Please explain What do u mean by expected number of couples? there may be as less as 1 or as many as
depending which is less. Do u want max. and min.
2
m
or
2
w
exploringnet
Mar 21 at 14:19
–
@exploringnet: No, the OP wants the
of the random variable
expected value
giving the number of couples in
seating
X
(
8
)
, where
8
ranges over all
8
seatings.
(
m
+
w
)!
Brian M. Scott
Mar 21 at 14:31
3 Answers
Consider a woman. If she’s sitting at one end of the row, there are
permutations in which she is part of a couple. Otherwise, there are
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