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    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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    Solution Summary

    This solution explains how to solve problems related to binomial coefficients and nonnegative integers.