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?

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- Oct 28th 2012, 08:50 AMSerillanCombination
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? - Oct 28th 2012, 01:49 PMPlatoRe: Combination
I have though about this question since it was posted.

The way it is written implies the use of*Pascal's Identity*

$\displaystyle \binom{N+1}{k}=\binom{N}{k-1}+\binom{N}{k}$.

But that lead nowhere that I can see.

Now $\displaystyle \binom{15}{3}-\binom{16}{2}=335$.

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