Question

A family has ninenine children. if this family has exactly threethree boysboysâ, how many different birth and gender orders areâ possible

Answer 1

This is the problem of how many permutations the set bbbgggggg has. The set has size n=9, and you choose p=3 boys.

You can calculate it as:

$\binom{9}{3} = \frac{9!}{3! \cdot 6!} = \frac{362880}{6\cdot720} = 84$