Question 1206503
<pre>
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</pre>