- Discrete Math
- Discrete Structures
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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This solution explains how to solve problems related to binomial coefficients and nonnegative integers.