Suppose that there are

distinct tyoes of coupons and each time one obtains a coupon it is, independent of prior selections, equally likely to be any one of the

types. One random variable of interest is

, the number of coupons that needs to be collected until one obtains a complete set of at least one of each type. Rather than derive

directly, let us start by considering the probability that

is greater than

. To do so, fix

and define the events

as follows:

is the event that no type

coupon is contained among the first

,

.

Hence,

I coulnd't understand the last equality, and why can't we derive

directly?

Appreciate those who help!!