SOLUTION: Calculate the number of ways in which three girls and four boys can be seated on a row of seven chairs if each arrangement is to be symmetrical.

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Question 1206503: Calculate the number of ways in which three girls and four boys can be seated on a row of seven chairs if each arrangement is to be symmetrical.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
A boy can't go in the middle, for that would leave an odd number of boys,
3, to be divided to go on both sides of him, which would not be symmetrical.
So 1 girl must go in the middle with 2 boys and 1 girl on each side of her.

To be symmetrical sex-wise, each arrangement must be in one of these 3 forms
sex-wise:

GBBGBBG, BGBGBGB, or BBGGGBB

In each of those 3 forms, the girls can be arranged 3! ways, and the
boys 4! ways: 

So the answer is (3)(3!)(4!) = 432 ways.

Edwin