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Five couples sit on a circular table for dinner. Two men out of these ten people sit adjacent to each other. Every husband sits adjacent to his wife. Find the total different combinations possible.

Five couples sit on a circular table for dinner. Two men out of these ten people sit adjacent to each other. Every husband sits adjacent to his wife. Find the total different combinations possible. Correct Answer 48

Given:

Five couples sit on a circular table for dinner

Two men out of these ten people sit adjacent to each other

Every husband sits adjacent to his wife

Concept:

n persons can be arranged in n positions in n! ways

Calculation:

Let the two men who sat adjacent be M1 and M2

W1 and W2 (wives of M1 and M2 respectively) will sit adjacent to M1 and M2 respectively

The couple sitting adjacent to W1 can be chosen in 3 ways

The couple sitting adjacent to W2 can be chosen in 2 ways

The three couples other than M1, W1 and M2, W2 can each be arranged in 2 ways

∴ Total number of ways = 3 × 2 × 2 × 2 × 2 = 48

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