Question 1192545: A school has 12 good runners of which 5 are girls. If four are chosen at random to represent the school in the district meet, what is the probability that the group will have at most three boys?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! number of ways to choose 4 from 12 is 12C4=495 ways
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0 boys, 4 girls has 5C4 or 5 ways
1 boy, 3 girls is 7C1*5C3=70 ways
2 boys, 2 girls is 7C2*5C2=210 ways
3 boys, 1 girl is 7C3*5C1=175 ways
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The answer is 460/495, the 460 being the sum of the four above, or 0.9293
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An easier way is to look at the probability of 4 boys, which is the only instance where there are not more than 3 boys, and that would be 7C4=35 ways out of 495, so the complement would be the answer.
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