# Male and Female Combinations Probability

• Oct 7th 2010, 01:15 PM
VitaX
Male and Female Combinations Probability
3 male and 3 female students will be sitting on these seats: A, B, C, D, E, and F. How many combinations can there be if exactly 2 girls have to sit on the left half (meaning exactly 2 girls have to be on the following seats: A, B and C)

My answer is 324 but I'm not sure if it is right.
• Oct 7th 2010, 01:30 PM
Quote:

Originally Posted by VitaX
3 male and 3 female students will be sitting on these seats: A, B, C, D, E, and F. How many combinations can there be if exactly 2 girls have to sit on the left half (meaning exactly 2 girls have to be on the following seats: A, B and C)

My answer is 324 but I'm not sure if it is right.

That's correct.

There are $\displaystyle\binom{3}{2}$ ways to choose the 2 girls for the left side.

There are $\displaystyle\binom{3}{1}$ ways to choose the boy.

Having made the choices, the remaining girl and 2 boys go on the right.

All that remains is to arrange both sides in all 3! ways for each side.

$\displaystyle\ (3!)^2\binom{3}{2}\binom{3}{1}=3^2(3!)^2=9(36)$