Take a simple example: .
To expand that product we take either x or y from each of the six factors.
In order to get we must take an x from each factor. That can be done in only one way.
But to get a term containing , we choose four x’s and two y’s.
We could do it as xxyxxy or yxxyxx for example. That can be done is ways.
In general, .
Just think about the number of ways to choose the terms from the n factors.