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## Homework Statement

A population has n men and n women. If you where to take 4 people out of the population to form a group what's the probability that there are exactly the same number of men as women in the group .

## Homework Equations

## The Attempt at a Solution

Ok so I thought of this to some extent and am lost.

The population size is 2n

(2n)(2n-1)(2n-2)(2n-3) different possible groups if you consider each person of the population to be distinct people without regards to the condition of gender.

When you take gender into consideration there are

2*2*2*2 = 2^4 = 16 different combinations when take the gender condition into account and consider each individual to be distinct (that is GGBB is different from BBGG)

If I consider each man and women to be the same there are a total of 5 different combinations...

BBBB

BBBG

BBGG

BGGG

GGGG

I know the following formula

P=(A|B) = [itex]\frac{P(A \bigcap B)}{P(B)}[/itex]

I'm assuming that I need to use this formula. The only problem is that I don't know how to come up with A and B.

Thanks for any help that nay one can provide.