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Inequality in factorials

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September 29, 2010
inequalitiesfactorialalgebracombinatoricscombinatorial inequalityIMO ShortlistIMO Longlist

Problem Statement

(CZS4)(CZS 4) Let K1,⋯ ,KnK_1,\cdots , K_n be nonnegative integers. Prove that K1!K2!⋯Kn!≥[Kn]!nK_1!K_2!\cdots K_n! \ge \left[\frac{K}{n}\right]!^n, where K=K1+⋯+KnK = K_1 + \cdots + K_n
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