Thursday, June 16, 2016

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.

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