The number of ways is which 6 men and 5 women can dine at a round table, if no two women are to sit together…
The number of ways is which 6 men and 5 women can dine at a round table, if no two women are to sit together is
$6 ! \times 5$ !
30
$5 ! \times 4$ !
$7 ! \times 5$ !
Solution
6 men can be seated in 5 ! ways
$[\because$ Number of ways in round table $=(n-1) !]$
Number of ways of placing women in between 6 men $=6 p_5=6$ !
Total number of ways $=5 ! \times 6 !$