# How many ways to distribute 6 notepads, 7 pencils and 8 markers?

In how many ways can you distribute six identical black notepads, seven identical red pencils and eight identical green markers to three students, so that each student gets at least one item of each kind?

I think the answer is: ${5 \choose 2}, then {6 \choose 2} and {7 \choose 2}$. Is this right? Do I have to multiply or just aggregate them?

## 2 Answers

Hint: http://en.wikipedia.org/wiki/Stars_and_bars_%28combinatorics%29 might be helpful to you.

This will tell you the number of ways to split up one of your items.

The answer for this question will be $\binom{6+3-1}6 \cdot \binom{7+3-1}7 \cdot \binom{8+3-1}8 = 48\cdot36\cdot28$.