Question 388108
The probability that a group of 5 chosen out of a group of 10 will contain exactly 2 girls and 3 boys is equal to:
(C(6,3) * C(4,2)) / C(10,5)


That becomes 120 / 252 = .476190476


That is the number of ways you can get a group of 5 consisting of 2 girls and 3 boys divided by the total number of ways you can get a group of 5.


It can also be calculated another way.


The probability of getting bbbgg (3 boys picked first and then 2 girls) would be:


6/10 * 5/9 * 4/8 * 4/7 * 3/6


This becomes .0476190476


You then need to multiply that by the number of different ways the group of 5 can be chosen.


That would be C(5,2) = 10


The total probability is therefore .0476190476 * 10 = .476190476


The number of ways the group of 5 can be choen is shown below:


bbbgg
bbgbg
bbggb
bgbbg
bgbgb
bggbb
gbbbg
gbbgb
gbgbb
ggbbb


bbbgg means boy drawn first and second and third girl drawn fourth and fifth.
bbgbg means boy drawn first and second girl drawn third boy drawn fourth girl drawn fifth.
etc. until you get to:
ggbbb means girls drawn first and second boy drawn third fourth and fifth.


both ways will get you the same answer.