# Sum of subsets

1. Jun 13, 2010

### soroush1358

Dear Friends,

I have a question and would be pleased if you help me by suggesting a paper or book to study.

Let A={1,2,....,n}. We consider all the subsets with k elements. How many of these sets have a sum of r ?
e.g.
for n=6, k=3, r=10

{1,3,6}

{1,4,5}

{2,3,5}
Hense the solution in this case is 3.

2. Jun 15, 2010

### Edgardo

Maybe this helps: http://en.wikipedia.org/wiki/Partition_(number_theory)" [Broken]

Last edited by a moderator: May 4, 2017
3. Jul 19, 2010

### Eynstone

It's the binomial coefficient (r-1) C (k-1).

4. Aug 18, 2010

### ross_tang

G_n(x,y) &= (1+x y)(1+x^2 y)(1+x^3 y)...(1+x^n y) \\ &= \prod_{r=1}^n (1+x^r y) \end{align*}