Tough GMAT PS question

[KL08]

26. Seven men and seven women have to sit around a circular table so that no 2 women are together. In how many different ways can this be done?
a.24 b.6 c.4 d.12 e.3

[wongee]

this takes me back to school, have to come back once someone posts the solution. Am still in the initia phases of studying, and these probs are my weakness.

Also, if someone can address how often these types of problems show up on the test, that would be great.

Thanks.

[samirpandeyit62]

Here in order to seat the men & women so that two women do not sit next to each other, we must seat the men & women alternativley.

Now if we take say a women as reference (coz there is no starting pt in a circular table) & seat others apropos her, then we can find the arrangements.

so the other 6 women can seat in 6 places in 6! ways apropos this women,

& 7 men can sit in 7! ways

so total is 6! * 7!

however this is not amongst the answer choices.

[wongee]

Can someone solve this question? Plss!

[ldoolitt]

Here in order to seat the men & women so that two women do not sit next to each other, we must seat the men & women alternativley.

Now if we take say a women as reference (coz there is no starting pt in a circular table) & seat others apropos her, then we can find the arrangements.

so the other 6 women can seat in 6 places in 6! ways apropos this women,

& 7 men can sit in 7! ways

so total is 6! * 7!

however this is not amongst the answer choices.

Good explanation. I agree.

To OP, are you sure you put the total text of the question and all the correct answer choices in there?

[neeraj_99]

i agree to pandey's explanation...it should be 6!*7!

[naren_nayak]

> so total is 6! * 7!
Samir,
Shouldn't that be 7! * 7! ?
The first seat you considered for the 1st woman can take 1 of 7 women so 7 * 6!
The only configuration in which 7 men and 7 women can be seated around a table so that no two women are seated next to each other is to alternate, as Samir said.
MWMWMWMWMWMWMW
The men can be shuffled around in their 7 seats in 7! ways and so can the women. So 7! * 7!
Does this make sense?