# Probability : Permutation and Position

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4. A group of individuals containing b boys and g girls is lined up in random order?that is, each of the (b + g)! permutations is assumed to be equally likely. What is the probability that the person in the ith position, 1 ≤ i ≤ b+g, is a girl?

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#### Solution Preview

The answer is g/(b+g).

Let's denote C(n,m)=n!/(m!*(n-m)!).

Because the b boys and g girls are lined up in random order. The ith position and the jth position make no difference. Thus for the ith position, we have g/(b+g) chance to put in ...

#### Solution Summary

A probability problem involving permutation and position is solved.

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