Distributing Presents Among Children

[squaremeplz]

Homework Statement

in how many ways can one distribute 15 identical gifts between 10 distinct children?

Homework Equations

(n + k - 1, k - 1) bionomail coeff.

The Attempt at a Solution

n = 15, k = 10

(24, 9) = 24!/(9!*15!)

It would be much appreciated if someone can verify my result. Thanks.

 

[Mark44]

I don't think what you have is right. I think the total number of ways is the sum of the binomial coefficients
(15 0) + (15 1) + (15 2) + ... + (15 10) where each one is n!/[(n - k)! k!]

My reasoning is this:
(15 0) - the number of ways to give all 15 gifts to no one--1 way
(15 1) - the number of ways to give all 15 gifts to 1 child--15 ways
(15 2) - the number of ways to give 15 gifts to 2 children (and hence none to the other 8)
And so on.
Anyway, that's how I would approach this problem.