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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 = kn 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 $m = kn$ then $k$ equals

Permutations and Combinations

Solution:

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