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Find the rook polynomial and an expression for the number of matchings of 5 men (rows)...

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Advance Math

Find the rook polynomial and an expression for the number ofmatchings of 5 men (rows) with 5 women (columns) given thefollowing forbidden pairings:
(M1,W4), (M2,W2), (M3,W3), (M4,W2), (M4,W4), (M5,W1), (M5,W3),(M5,W45).

Answer is 5! - 8x4! + 21x3! - 20x2!+ 6x1!, please explain how toget it, thanks.

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