1. Combination

I need to write this expression with one combination number: C(15,3)-C(16,2)=C(n,k) so I need to find n and k
How can i get one from these two without using factorials?

2. Re: Combination

Originally Posted by Serillan
I need to write this expression with one combination number: C(15,3)-C(16,2)=C(n,k) so I need to find n and k
How can i get one from these two without using factorials?
I have though about this question since it was posted.
The way it is written implies the use of Pascal's Identity
$\binom{N+1}{k}=\binom{N}{k-1}+\binom{N}{k}$.

But that lead nowhere that I can see.

Now $\binom{15}{3}-\binom{16}{2}=335$.
So I did a rather large computer search on various combinations $\binom{N}{k}$ but found none to equal 335. I thought that finding one might give a clue as to how that identity might apply.