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139.A Weighted Hockey-Stick Sum

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combinatoricsCh. 1 — Classical Probability and Combinatorics444+ Problems in Probability
Evaluate 12(33)+11(43)+10(53)+⋯+2(133)+(143).12\binom{3}{3} + 11\binom{4}{3} + 10\binom{5}{3} + \cdots + 2\binom{13}{3} + \binom{14}{3}.

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