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The science club has 25 members: 10 boys and 15 girls. A 5-person committee is chosen at random. What is the probability that the committee has at least 1 boy and at least 1 girl?

Guest Jun 13, 2017

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The total number of committees that can be formed = C(25,5)  = 53130

And from this we just want to subtract all the commitees that can  be formed solely of boys  = C(10,5) = 252 and all the committees that can be formed solely of girls  = C(15,5)  = 3003

So.....the probability of a committee with at least one boy and one girl  =

[ 53130 - 252 - 3003] / 53130  = .9387  = 93.87%

CPhill  Jun 13, 2017
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#1
+81022
+1

The total number of committees that can be formed = C(25,5)  = 53130

And from this we just want to subtract all the commitees that can  be formed solely of boys  = C(10,5) = 252 and all the committees that can be formed solely of girls  = C(15,5)  = 3003

So.....the probability of a committee with at least one boy and one girl  =

[ 53130 - 252 - 3003] / 53130  = .9387  = 93.87%

CPhill  Jun 13, 2017

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