Math Help - Permutation and Combinations

1. Permutation and Combinations

How many ways are there to distribute n candies to k kids such that no child gets more than m − 1 candies.

"select this from this, then choose this from this"
sentence for me, and then I will write an equation.

2. Originally Posted by DeRSeD
How many ways are there to distribute n candies to k kids such that no child gets more than m − 1 chocolates.
candies or chocolates.

What is going on?

3. Originally Posted by Plato
candies or chocolates.

What is going on?
Sorry.

My mistake.

4. Originally Posted by DeRSeD
Sorry.

My mistake.
Consider

$x_1 + x_2 + .... + x_k = n$

Where each of the $0<=x_i

Number of ways to distribute the chocs is number of solution to the above equation.

Now consider the expansion of $(1+x^2+....+x^{m-1})^k$