If 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
Question
If 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
Solution
The problem can be solved using the concept of permutations and combinations.
Step 1: Arrange the 'm' men in a row. The number of ways to do this is m!.
Step 2: There are now 'm+1' spaces (before, between, and after the men) where we can place the 'n' women such that no two women are next to each other.
Step 3: The number of ways to choose 'n' spaces from 'm+1' spaces is C(m+1, n).
Step 4: The number of ways to arrange 'n' women in 'n' spaces is n!.
Step 5: By the multiplication principle, the total number of ways to arrange the men and women is m! * C(m+1, n) * n!.
So, the number of ways in which they can be seated is m! * C(m+1, n) * n!.
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