The number of ways of arranging 8 men and 4 women around a circular table such that no two women can sit together, is

Question

The number of ways of arranging 8 men and 4 women around a circular table such that no two women can sit together, is (A) 8! (B) 4! (C) 8!4! (D) 7! 8P4

Tardigrade Admin · Accepted Answer

The number of ways of arranging 8 men =7! The number of ways of arranging 4 women such that no two women can sit together = 8 P4 ∴ Required number of ways =7 ! 8P4

Q. The number of ways of arranging $8$ men and $4$ women around a circular table such that no two women can sit together, is

$8!$

$4!$

$8! 4!$

$7!^{8} P_{4}$

The number of ways of arranging $8$ men $= 7!$
The number of ways of arranging $4$ women such that no two women can sit together $=^{8} P_{4}$
$∴$ Required number of ways $= 7!^{8} P_{4}$

Q. The number of ways of arranging 8 men and 4 women around a circular table such that no two women can sit together, is

8!

4!

8!4!

7!8P4​