Permutations And Combinations Question 25
Question: $ m $ men and n women are to be seated in a row so that no two women sit together. If $ m>n $ , then the number of ways in which they can be seated is [IIT 1983]
Options:
A) $ \frac{m\ !\ (m+1)\ !}{(m-n+1)\ !} $
B) $ \frac{m\ !\ (m-1)\ !}{(m-n+1)\ !} $
C) $ \frac{(m-1)\ !\ (m+1)\ !}{(m-n+1)\ !} $
D) None of these
Correct Answer: A
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Answer:
Solution:
$ \therefore $ By the fundamental theorem, the required number of arrangements of m men and n women $ (n<m) $ = $ m!{{.}^{m+1}}P _{n}=\frac{m!.(m+1)!}{{(m+1)-n}!}=\frac{m!(m+1)!}{(m-n+1)!} $ .
BETA
