Question

In how many ways can $8$ persons consisting of $4$ men and $4$ women can be seated round a table if no two men are to be in adjacent seats.

• A. $4!\times 4!$
• B. $7!$
• C. $3!\times 4!$
• D. $8!$

Answer 1

The correct option is C $3!\times 4!$

$8$ Persons

Let the men be seated first

$=(4-1)!=3!=6$

Number of place for women $=4$

$4$ women are there

Therefore number of ways $=4!$

Total ways $=4!\times 3!$