Question

find the number of ways of arranging 8 men and 4 women around a circular table
a)all the women sit together
b)no two women sit together
c)no two men sit together

Answer 1

Answer:

Numbers of ways such that no two women. sit together is such that to first arrange all the men in a circle and then place the women in places between them

umber of ways of arranging 8 men in a circle is (n−1)!=(8−1)!=7!

number of ways of placing 4 women in 8 places between men is  

$^{8}P_{4}$

​∴ Total numbers of ways= $^{8} P_{4}$×7! = $7!^{8} P_{4}$