We have where and
There are several ways to solve this.
1. We first consider the number of possibilities without the restriction
We have (1) ways
Now we will consider the restriction, indeed if we have to substract the cases in which from (1)
So there are ways to do this.
Therefore the final answer would be
2. By Generating Functions
Note that it is the coefficient of in the product
This is easy to calculate
By the Binomial Theorem: so
Then the coefficient is
(Here notice that again we are substracting the extra we'd have without the restriction)