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 __________.

Answer 1

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 +1}P_n
∴ Total number of ways of seating men and women is m! (^{m + 1}P_n)
$\mathrm{i}.\mathrm{e}m!\frac{\left(m+1\right)!}{\left(m+1-n\right)!}$