random variables - Probability of having at least one coupon out of N types

I'm facing a question regarding random variables:

A coupon website has N distinct kinds of coupons. Each selection of a
coupon is equally likely and selections are independent. Let $T$ be a random variable representing the number of
coupons, $n$, that one should collect until he has at least one coupon
of every kind.

I need to determine the probability function $P(T=n)$. How should I approach this question?