[JEE Advanced 1983] m men and n women m n sit in a row with no two
$m$ men and $n$ women ($m>n$) sit in a row with no two women together. Show the number of ways is $\dfrac{m!\,(m+1)!}{(m-n+1)!}$.
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· 2d ago
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Answer: Proved.
Arrange the men: $m!$. They create $m+1$ gaps; seat the women in $n$ of them: $^{m+1}P_n=\frac{(m+1)!}{(m-n+1)!}$. Product gives the result.
JEE Advanced 1983 · Permutations and Combinations — verified solution by the Vidaara Team.
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