Question

A family has seven children. If this family has exactly two boys, how many different birth and gender orders are​ possible?

There are _____. different birth and gender orders possible.

Answer 1

This is the combination problem .

_n C _x = n! / x!(n - x)!

n! = n(n - 1)(n - 2) .... and so on .

n = 7 and x = 2

₇ C ₂ = 7! / 2!(7 - 2)! = 7! / 2!(5)! = 21

There are 21 different birth and gender orders possible.