Find the number of ways of arranging 8 men and 4 women around a circular table. In how many of them
no two women come together

Explanation

Total number of persons = 12 (8 men +4 women)
Therefore, the number of circular permutations is (11) !
First arrange 8 men around a circle in 7! Ways. Then there are 8 places in between them as shown in fig by the symbol x (one place in between any two consecutive men).
Now the 4 women can be arranged in these 8 places in `""^(8)P_(4)` ways.

Therefore, the number of circular arrangements in which no two women come together is `7! xx""^(8)P_(4)`.