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  4. 3 Indian and 3 American men and their wives are to be seated round a circular table. Let m denotes the number of ways when the Indian couples are together and n denotes the number of ways when all the six couples are together. If m= k n then k equals

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Q. 3 Indian and 3 American men and their wives are to be seated round a circular table. Let $m$ denotes the number of ways when the Indian couples are together and $n$ denotes the number of ways when all the six couples are together.
If $m= k n$ then $k$ equals

Permutations and Combinations

Solution:

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$ m =8 ! 2^3 $
$n =5 ! 2^6 $
$\frac{ m }{ n }=\frac{8 \cdot 7 \cdot 6 \cdot 5 ! \cdot 2^3}{5 ! \cdot 2^6} $
$k =42 $