Q: How many different basketball teams of 5 people can be chosen from 10 people?

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I figured out the answer: 18+7 = 25, So 25C5 = 53,130 Teams. This assumes there are no sex restrictions on the teams (for example, "teams must include at least one boy and at least one girl"). That would be a lot more complicated, and if that's a factor you'd need to specify exactly what the restrictions are.

This is what I got: 18C3 * 7C2 + 18C4 * 7C1 + 18C5 * 7C0 = 47,124 Is this right?

37 ÷ 5 = 7 remainder 2 → You can make 7 teams, but have 2 children left out. However, if you meant you have a pool of 37 children and need to make a team consisting of 5 children from that 37, then how many different teams (or groups) of 5 children you can make then: This is a combination as the order of selection doesn't matter, only which 5 children are chosen. Here you can make: 37 C 5 = 37!/((37-5)!5!) = (37 × 36 × 35 × 34 × 33)/(5 × 4 × 3 × 2 × 1) = 435,897 different teams

18

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