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