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Three married couples sit in a row. Find...

Three married couples sit in a row. Find the probability that no husband sits with his wife.

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Total number of cases = 6! = 720
Number of favourable cases
= Total number of cases - Cases when at least one husband sits with his wife
`=6! - (.^(3)C_(1)xx2!xx5! - .^(3)C_(2)xx2! xx2! xx4! + .^(3)C_(3) xx 2! xx 2! xx2! xx3!)` (Using principle of Inclusion - Exclusion)
= 720 - (720 - 288 + 48) = 240
`therefore` Required probability = `(240)/(720) = (1)/(3)`
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