- #1
twoflower
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Homework Statement
Let's have 2n persons, n men and n women. Suppose they sit randomly around a table with 2n chairs. What is the probability that no two persons of the same sex will sit next to each other?
The Attempt at a Solution
Here's my idea:
I will model this situation with classic probability. The set of all possible events (ie. the ways the people will sit around the table) is set of all strings consisting of 'W' and 'M' of length 2n. The only strings which satisfy our condition is
WMWMWM...WM
and
MWMWMW...MW
Number of all possibilities is [itex]2^{2n}[/itex], ie. the probability will be
[tex]
\frac{1}{2^{2n-1}}
[/tex]
Is this solution correct?