Answer:
There are 64 possible birth orders in a family with six children.
Step-by-step 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 [tex]2^{n}[/tex] birth orders.
In this problem, we have that:
The family has 6 chilren.
So there are [tex]2^{6} = 64[/tex] possible birth orders.
