Three couples sit for a photograph in 2 rows of three people each such that no couple is sitting in the same row next to each other or in the same column one behind the other. How many arrangements are possible?

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Quantrex Academy · Accepted Answer

Correct answer: 96

Case-1 : Both rows have no couple, i.e. 2 C₁ 2 C₁ 2 C₁ 31 3! (1- 1 1! + 1 2! - 1 3! )=96 Case-II : Both rows have exaclty 1 couple 3 C₁ 2 C₁ 2 C₁ 2! 2! 0=0 cases Total cases =96

Three couples sit for a photograph in 2 rows of three people each such that no couple is sitting in the same row next to each other or in the same column one behind the other. How many arrangements are possible?

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