For the white balls:

Order does not matter, so the number of possibilities can be represented by a combination.

There are possible choices and we are choosing .

Formula for the number of all combinations of  things, taken  at time is  .

Find the combinations of white balls taken at a time.

Substitute in .

.

For the red ball, there are possible choices and we are choosing .

Substitute in .

The Fundamental Counting Principle :

.

Therefore, the total number of possibilities is

.

.