Question 388108: There are 6 boys and 4 girls and a group of 5 people must be formed. How many groups are possible consisting of 2 girls and 3 boys
Answer:
nCr=combination of n things taken r at a time= n!/((n-r)!*r!)
4C2 * 6C3
=6*20
=120 groups
If a group is chosen randomly from the 10 people, find the probability that the group will consist exactly of 2 girls and 3 boys.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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