circular permutation

[sjpre10]

Eight men and two women are to be seated around a table. In how many ways can they be arranged if the two women are not sit directly opposite one another.

Please explain.

[sharathn]

Hi,

8 Men and 2 Women can be seated around the table in (10-1)! ways.

No of ways you can arrange 2 women around a table sitting opposite to each other = 10
No of ways we can arrange 8 men = 8!
totoal no of ways you can arrange 8 men and 2 women where the 2 women sitting opposite to each other = 10 * 8!
total no of ways you can arrange 8 men and 2 women around a table, where the 2 women are not sitting opposite to each other = 9! - 10 * 8!

Thanks,
Sharath