(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A team consisting of three boys and four girls must be formed from a group of nine boys and eight girls. If two of the girls are feuding and refusing to play on the same team, how many possibilities do we have?

2. Relevant equations

Combination formula [itex]\binom{n}{r}=\frac{n!}{(n-r)!r!}[/itex]

3. The attempt at a solution

My logic was that there are [itex]\binom{9}{3}[/itex] ways to choose the boys. For the girls I am a bit confused on how I would approach it. There are [itex]\binom{6}{4}[/itex] ways of choosing with only one of the girls who are fighting. But I do not know where to go from here.

The solution says..

[itex]\binom{9}{3}\left[ \binom{6}{4}+2\binom{6}{3} \right][/itex]

Almost got it, but I do not understand the logic behind the second term in the brackets.

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# Homework Help: This solution doesn't make sense to me (Probability)

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