In how many different ways can you seat 11 men and 8 women in a circle?b. In how many different ways can you seat 11 men and 8 women in a row if the men all sittogether and the women all sit together?c. In how many different ways can you seat 11 men and 8 women in a row if no 2 women areto sit together?

a)  6.402373706 × 10¹⁵

b) 1.609445376 × 10¹²

c) 7.966754611 × 10¹⁴

Step-by-step explanation:

a) Since they are 11 men and 8 women to be seated in a circle  and they can be arranged in any manner.

Therefore the total number of men and women = 11 men + 8 women = 19 people.

Since they are to be seated in a circle, the number of ways this can happen = (19 - 1)! = 18! = 6.402373706 × 10¹⁵

b) 11 men and 8 women in a row if the men all sit together and the women all sit together

First, the women are arranged in one group. 8 women can be seated in 8! ways.

The 11 men can be seated in the remaining 11 places in 11! ways

Therefore the number of arrangements = (11! × 8!) arrangements

                                                                  = 1.609445376 × 10¹²

c) If no 2 women sit together, that means between two men, there is at most 1 woman.

Firstly, we consider the position of the men. The number of ways 11 men can be arranged in a row =

Now as no two women stand next to each other,we can imagine the situation as:

*M*M*M*M*M*M*M*M*M*M*M*

To find how many ways we can arrange 8 women in the 12 possible places (as shown above) =

Using product rule, the number of arrangements = 39916800 × 19958400 = 7.966754611 × 10¹⁴

12/11c

or

12

c

11