SOLUTION: There are 20 students in a class, 10 who are girls, and 10 who are boys. The teacher is choosing 4 of these students to be on a committee. What is the probability that there will b

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Question 614921: There are 20 students in a class, 10 who are girls, and 10 who are boys. The teacher is choosing 4 of these students to be on a committee. What is the probability that there will be at least one girl and at least one boy? Use complementary counting.
Answer by stanbon(75887) About Me  (Show Source):
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There are 20 students in a class, 10 who are girls, and 10 who are boys. The teacher is choosing 4 of these students to be on a committee. What is the probability that there will be at least one girl and at least one boy? Use complementary counting.
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Number of ways to fail:
Choose 4 boys: 1 way
Choose 4 girls: 1 way
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# of possible groups of 4: 20C4 = 4045
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P(at lest one boy and at least one girl) = 1 - 2/4045 = 4043/4035
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Cheers,
Stan H.
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