Permutations and Combinations 2 Question 23

23. 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)!

(1983, 2M)

Show Answer

Answer:

Correct Answer: 23. (n=9 and r=3)

Solution:

  1. Since, m men and n women are to be seated in a row so that no two women sit together. This could be shown as

×M1×M2×M3×…×Mm×

which shows there are (m+1) places for n women.

∴ Number of ways in which they can be arranged

=(m)!m+1Pn=(m)!⋅(m+1)!(m+1−n)!

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