Question

m Men and n women are to be seated in a row, so that no two women sit together. If m > n , then find the number of ways in which they can be seated.

Answer 1

First arrange m men, in a row in m! ways. Since n < m and no two women can sit together, in any one of the m! arrangement, there are (m + 1) places in which n women can be arranged in  ^{m + 1}P_n ways.

Therefore, by the fundamental theorem, the required number of arrangement is