Question 907939: How many different teams of 4 children can be chosen from a group of 19 girls and 17 boys if each team must have at least two boys in it?
I think it would be nCr(36,4)/[nCr(17,2)*nCr(17,3)*nCr(17,4)]
So you need teams of 4(numerator)
and you need a minimum of two boys so exhaust all combinations(denominator)
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website!
First we'll find the number of teams of 4 from the 36 children without
restrictions of gender. Then we'll subtract the number with no boys
and the number with just 1 boy.
1. The number of teams with no restriction of gender.
That's 36C4 = 58905 teams with no restrictions of gender.
2. The number of teams with no boys, which means 4 girls:
That's 19C4 = 3876 teams of all girls, no boys, which we must subtract.
3. The number of teams with exactly 1 boy and 3 girls:
We can choose the 1 boy 17C1 = 17 ways.
Then we can choose the 3 girls 19C3 = 969 ways.
Thats 17(969) = 16473 ways, which we also must subtract.
Final answer = 58905-3876-16473 = 38556 teams with at least 2 boys.
Edwin
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