another permutation toughie

[shrutiashok@chennai]

seven men and seven women have to sit around a circular table so that no 2 women are together. how many ways?

Ans a.24
b.6
c.4
d.12
e.3

[awhig]

I suggest to first arrange men. This can be done in 6! ways. Now to satisfy above cond. for women, they should sit in spaces between each man. This can be done in 7! ways ( because there will be seven spaces between each man on round table).Since women = men this is the only case i am getting.

Total ways = 6! * 7! [Acc. to me]

[gmatguy]

its 6! *7!

[GMAT-HELP]

seven men and seven women have to sit around a circular table so that no 2 women are together. how many ways?

Ans a.24
b.6
c.4
d.12
e.3

Plz check ur ans choices. I went thru' the source and these ans choices are for a different qn.
The ans is 6!*7! for the qn above.


Thanks,
GMAT-HELP

[ruhi160184]

I saw this problem somewhere else too with the same answer choices. Well the answer choices are wrong. ITs 7!*6!

[adonis7881]

i concur answer is 7!*6!

[Brasileiro]

[QUOTE=awhig]I suggest to first arrange men. This can be done in 6! ways.

Why in 6! ways and not in 7! ways?

thanks in advance for the explanation

Bras

[araspee]

because you have (n-1)! ways to arrange the men or women in a circle. Once the men or women are arranged you can seat the women or men between them in n!ways just like arranging in a row.

[lorcar]

PLZ; would some be so kind to explain the difference between this example and the example in the other thread, where they seat in a row, but also alterantively?

here we should subtract the cases where the combination is just a "rotation" of table?

[ashok_sharma]

seven men and seven women have to sit around a circular table so that no 2 women are together. how many ways?

Ans a.24
b.6
c.4
d.12
e.3

answer is 6!7!