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# counting problem

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4 girls and 8 boys are standing together. In how many ways can a 7- person committee be selected from the group if at least 2 girls must be included?

Jul 25, 2020

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So it is an example of what will not work!

Take 2 girls first     4C2

then take 5 from what is left      10C5

That is assuming all committee members are equal.

Jul 25, 2020
edited by Melody  Jul 25, 2020
edited by Melody  Jul 25, 2020
#2
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melody that is incorrect

Guest Jul 25, 2020
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Melody  Jul 25, 2020
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when you choose 2 girls then 5 other members you overcount (you can choose all 4 girls by choosing the first two, then choosing the other 2 girls and other 3 boys when you choose the other five, OR by choosing the last two girls first, then choosing the first two girls +other 3 boys)

Guest Jul 25, 2020
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Yes thank you, I can see that your are correct, I have overcounted

So I needed to looked at the 3 scenarios separately and then add the probablities together.

2 girls+5 boys

3 girls+ 4 boys

4 girls + 3 boy

Melody  Jul 25, 2020
edited by Melody  Jul 25, 2020