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# The science club has 25 members: 10 boys and 15 girls.

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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?

Feb 25, 2018

#1
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But, you could also do the following which gives you the same answer:

P(boys) =10/25 x 9/24 x 8/23 x 7/22 x 6/21=30,240 / 6,375,600 =6 / 1265

P(girls) =15/25 x 14/24 x 13/23 x 12/22 x 11/21 =360,360 / 6,375,600 =13 / 230

6/1265 + 13/230 =31 / 506

The probability of at least 1 boy and 1 girl on a 5-person committee is:

1 - [31 / 506] = 475 / 506 = 93.87%

Feb 25, 2018

#1
+1

But, you could also do the following which gives you the same answer:

P(boys) =10/25 x 9/24 x 8/23 x 7/22 x 6/21=30,240 / 6,375,600 =6 / 1265

P(girls) =15/25 x 14/24 x 13/23 x 12/22 x 11/21 =360,360 / 6,375,600 =13 / 230

6/1265 + 13/230 =31 / 506

The probability of at least 1 boy and 1 girl on a 5-person committee is:

1 - [31 / 506] = 475 / 506 = 93.87%

Guest Feb 25, 2018