Answer:
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 = [tex]^{11} P_{11}=\frac{11!}{(11-11)!} =11!=39916800[/tex]
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) = [tex]^{12} P_{8}=\frac{12!}{(12-8)!} =19958400[/tex]
Using product rule, the number of arrangements = 39916800 × 19958400 = 7.966754611 × 10¹⁴
