If there are $12$ people in the room what the chances are that no two people will have the same birthday month?
I tried to think of it in this way:
The total number of options is $12^{12}$
The option that no one will have the same birthday month is:
$12 * 11 * ... 1$ which means $12!$
So I think the answer is:
$$\frac{12!}{12^{12}}=0.0000537$$
What do you think?
Thank you!