Combinatorics: $N$ couples sitting in a row, $M$ couples in the $N$ couples can't sit together.
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$N$ couples sitting in a row, $M$ couples in the $N$ couples can't sit together. How many ways are there to arrange the seat? This is a variation of ménage problem, I thought I could arrange the M couples first using ménage problem's solution(https://www.math.dartmouth.edu//~doyle/docs/menage/menage/menage.html), but then it does not count ACaBcb, where $M=2$ (that is Aa, Bb) and $N=3$ . Thanks! It is not necessary that women and men alternate, AC aB cb
combinatorics
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edited Nov 18 at 7:56
Robert Z
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