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ISI2021-MMA: 25

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Two rows of $n$ chairs, facing each other, are laid out. The number of different ways that $n$ couples can sit on these chairs such that each person sits directly opposite to his/her partner is

  1. $n!$
  2. $n! / 2$
  3. $2^{n} n!$
  4. $2 n !$
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  1. 2^n n! .
  2. Let’s consider each couple as 1 until Then we have n couples and n seats so total we arrange them in n! ways. Now each couple can we arrange in themselves in 2! ways. So as there are n couples total is n!*2^n.
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