Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together.

Question

Philoid · Accepted Answer

6 men can be arranged in (6-1)! = 5! ways to dine at a round table.

Now, if we place 5 women in 6 empty seats between them so that no two women will be together, and this can be done in ⁶P₅ ways i.e. in

As, the operations are dependent, so, the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together.

=5!×6!

The discussion can be shown pictorially as:

[X = 6 empty seats between the 6 men(M)]