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Counting & ProbabilityEasyIdentities and Techniques, Proved

Identities and Techniques, Proved · Easy problem

The committee–chair identity says k(nk)=n(n−1k−1)k\binom{n}{k}=n\binom{n-1}{k-1}. Find the integer mm with 0≤m≤50\le m\le 5 for which 5(125)=12(11m)5\binom{12}{5}=12\binom{11}{m}.