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An inequality on grid cell

Source: Tuymaada 2019 P7 out of 8

July 15, 2019
inequalitiesgrid

Problem Statement

NN cells chosen on a rectangular grid. Let aia_i is number of chosen cells in ii-th row, bjb_j is number of chosen cells in jj-th column. Prove that ∏iai!⋅∏jbj!≤N! \prod_{i} a_i! \cdot \prod_{j} b_j! \leq N!
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