The number of ways to seat n couples around a circular table such that no couple sits next to each other is 2n * n! ways.
What are permutation and combination?
Combination and permutation are two different ways of grouping elements of a set into subsets in mathematics. The elements of the subset can be listed in any order in a combination. The elements of the subset are listed in a specific order in a permutation.
There are 'n' couples.
There are 'n' men and 'n' women
n men can be arranged in n! ways.
and 'n' women can be arranged in 2*n ways.
The total number of ways = 2*n * n! ways.
Hence, the number of ways to seat n couples around a circular table such that no couple sits next to each other is 2n * n! ways.
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