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**1. 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?

**3. 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?