# Binomial coefficients and nonnegative integers

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Prove the identity (n~r) (r~k) = (n~k) ((n-k)~(r-k)), whenever n, r, and k are nonnegative integers with r less than/equal to n and k less than/equal to r:

a) using a combinatorial argument.

b) using an argument based on the formula for the number of r-combinations of a set with n elements.

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Â© BrainMass Inc. brainmass.com December 24, 2021, 10:52 pm ad1c9bdddf>https://brainmass.com/math/discrete-structures/binomial-coefficients-nonnegative-integers-514202