This is the question of circular permutations

therefore the formula is (n-1)!

For example,
if you want to arrange 5 people in a circular table, how many ways can you do that?

Since we are dealing with circular position, you fix 1 person, which can be done in 1 way. Now arrange 4 people in the circle. This can be done in 4! ways

total no. of ways = 4! * 1 = 4! = 24, which is same as the formula, (5-1)! = 4! = 24


Now coming to the question:

arrange 7 men and 7 women, so that no 2 women are sitting together.

This can be done in 2 ways, logic is the same though

Method 1

Fix 1 man, remaining 6 men can be arranged in 6! ways

Now arrange 7 women between 6 men, this can be done in 7! ways

total ways = 6! * 7!

Method 2

Fix 1 woman, remaining 6 women can be arranged in 6! ways
now arrange 7 men between 6 women so that no 2 women can sit together = 7! ways

total ways = 7! * 6!

Hope this helps.

thanks a lot ,

I understand the explanation, but why doesn't it match up with any of the answer choices?

jsk988 wrote:I understand the explanation, but why doesn't it match up with any of the answer choices?

I believe the answer options are incorrect.