Number of ways in which maried couples can be seated round a table such that men and women are alternate and not all women adjacent to her husband,is...
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Number of ways men and women can be seated alternately = 8 4 ! × 4 ! × 2 ! = 1 4 4
And number of ways by which all women gets seated adjacent to her husband = 8 4 ! × 2 ! × 2 = 1 2
hence the number of ways in which 4 maried couples can be seated round a table such that men and women are alternate and not all women adjacent to her husband = 1 4 4 − 1 2 = 1 3 2