A store sells 4 different kinds of Tshirts of your size In h

A store sells 4 different kinds of T-shirts of your size. In how many different ways can you buy ten T-shirts? How many different combinations of ten T-shirts will have at least one of each kind?

Solution

a)

In how many different ways can you buy ten T-shirts?

There are 4 kinds, so there are 4^10 = 1048576 ways. [ANSWER]

*****************************

B)

How many different combinations of ten T-shirts will have at least one of each kind?

We first fix that there is already one of each kind.
So we can do what we want with the other 6.

Thus, there are 4^6 = 4096 WAYS. [ANSWER]