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m men and n women are to be seated in a row so that no two women sit together. If m > n then show that the number of ways in which they can be seated is m! (m + 1)!/(m – n + 1)!

m men and n women are to be seated in a row so that no two women sit together. If m > n then show that the number of ways in which they can be seated is m! (m + 1)!/(m – n + 1)!

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
6 years ago
Hello Student,
Please find the answer to your question
m men can be seated in m! ways creating (m + 1) places for ladies to sit.
n ladies out of (m + 1) places (as n < m) can be seated in m + 1 Pn
∴ Total ways = m! x m + 1 Pn
= m! x (m + 1)!/(m + 1 – n)! = (m + 1) 1m! / (m – n + 1)!

Thanks
navjot kalra
askIITians Faculty

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