Question

How many possible birth orders with respect to gender are possible in a family with six ​children

Answer 1

There are 64 possible birth orders in a family with six children.

Explanation:

Let's start from 1 children.

You can have M or F. So two possible birth orders.

With two children, you can have M-M, M-F, F-M, F-F. So 2^2 = 4 possible birth orders.

For three children.

M-M-M, M-M-F, M-F-M, M-F-F, F-M-M, F-M-F, F-F-M, F-F-F. So 2^3 = 8 possible birth orders.

Generalizing:

For n children, you can have
`2^(n)` birth orders.

In this problem, we have that:

The family has 6 chilren.

So there are
`2^(6) = 64` possible birth orders.