In how many different ways 3 girls and 3 boys be seated at..

Hi LUANDATO,

We're told that 3 girls and 3 boys will be seated at a rectangular table that has 3 chairs on one side and 3 stools on the other side, and that two girls or two boys can never sit side-by-side. We're asked for the number of possible arrangements of the 6 children. While there are several ways to approach this question, it's ultimately a Permutation question.

To start, I'll label the seats....
ABC
DEF

ANY of the 6 children can sit in Seat A. Once we place one.....
There are 3 possible options for Seat B (since the opposite GMAT has to sit here). Once we place one...
There are 2 possible options for Seat C (the same GMAT that sat in Seat A). Once we place one....
There are 2 possible options for Seat D (the same GMAT that sat in Seat B). Once we place one....
There are 1 possible options for Seat E (the same GMAT that sat in Seat A and C).
There are 1 possible options for Seat F (the same GMAT that sat in Seat B and D).

Total arrangements = (6)(3)(2)(2)(1)(1) = 72

Final Answer: C

GMAT assassins aren't born, they're made,
Rich