The number of ways in which 5 women and 3 men are to be seated at a round table so that no two men are to sit together is:

Question

Question

Answer 1

Concept:

Permutation: Permutation is defined as arrangement of r things that can be done out of total n things. This is denoted by ⁿP_r:

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

Calculation:

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

Now, 5 space generated between the women.

Where w1 denotes the position of women and X denotes the space.

Then 3 men sit on the 5 space generated between the women which can be done in ⁵P₃ ways

Hence total number of ways is = 4! × ⁵P₃ = 24 × 60 = 1440 ways