Question

The number of ways in which 5 men and 3 women are to be seated at a round table so that no two women are to sit together is:
1. 5! × 5P3
2. 4! × 5P3
3. 4! × 6P3
4. None of these

Answer 1

Correct Answer - Option 2 : 4! × 5P3

Concept:

n different objects are arranged around a circle, then the number of arrangements is (n – 1)!

Calculation:

First, arrange 5 men at the round table in (5 - 1)! ways = 4!

Now, women sit on the 5 spaces generated between the men

This can be done in ⁵P₃ ways

Hence the total number of ways is = 4! × 5P3