# The number of ways 'm' men and 'n' women (m > n) can be seated in arow so that no two women sit together is

Question:

The number of ways 'm' men and 'n' women (m > n) can be seated in arow so that no two women sit together is __________.

Solution:

m men can be arranged in m! ways

Since no two women are to be together

⇒ we have m + 1 places for women

∴ out of m + 1 places, places to be taken = n

i.e, the women can be seated in m +1Pn

Total number of ways of seating men and women is m! (m + 1Pn)

i. e $m ! \frac{(m+1) !}{(m+1-n) !}$