Probability of birthday month Question: In a class of $12$ students, what is the probability that each student was born in a different month?
Approach: would it be $\left(\frac{1}{12}\right)^{12}$?

It would be $\frac{11!}{12^{11}}$
Reason: For the first person, he can have any month as their birthday, of which the probability = $1$. For the second person, they need to have their birthday in a month that was the previous person's birthday month, of which probability is $\frac{11}{12}$. Using the same logic, you can go on to the last person, who only has one choice, of which probability $\frac{1}{12}$.
