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# Counting problem

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My school's math club has 6 boys and 8 girls. I need to select a team to send to the state math competition. We want $$7$$ people on the team. In how many ways can I select the team to have 3 boys and $$4$$ girls?

Feb 7, 2022

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There are $${6 \choose 3 }= 20$$ ways to choose 3 boys for the team

There is $${8 \choose 4} = 70$$ ways to choose 4 girls for the team

Thus, there are $$20 \times 70 = \color{brown}\boxed{1400}$$ ways to choose 3 boys and 4 girls for the team.

Feb 7, 2022