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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

A
m!(m+1)!(mn+1)!
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B
m!(m1)!(mn+1)!
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C
(m1)!(m+1)!(mn+1)!
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D
None of these
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Solution

The correct option is D m!(m+1)!(mn+1)!
m men can be arranged in m seats =m! ways.
After m men be seated, we mat get one seat in the beginning and one seat in the end and (m1) seats bet n each pair of men for the women .
Thus the no. of ways which n women can be seated in (m1+1+1)=(m+2) seats =m+1pn
total numbers of arrangement =(m)!×m+2pn
=(m!)(m+1)!(m+2n)!
=(m!)(m+1)!(m.n+D)!

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