Friday, November 1, 2019

combinatorics - Find a Summation Formula for nCr

There was a previous problem in my homework that basically demonstrated that:



10C7 = 9C6 + 8C6 + 7C6 + 6C6

And our question is:


"Use that fact to derive a summation formula involving expressions nC1."

I'm not entirely sure what this means, but I'm assuming we are to use Sigma. This is what I came up with:


$${}_nC_r = \sum_{i=r - 1}^{n-1} {}_iC_{r-1}$$


I'm not sure if I'm even using legal notation here, so any help would be greatly appreciated.

No comments:

Post a Comment

analysis - Injection, making bijection

I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...