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How many ways can a 3-person subcommittee be selected from a committee of 7 people?
Wiki User
∙ 13y ago
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Clara Lebsack
Wiki User
∙ 13y agoThe first selection can be any one of 7 people.
The second one can be any one of the remaining 6.
The third one can be any one of the remaining 5.
So the subcommittee can be selected in (7 x 6 x 5) = 210different ways.
But ... there aren't that many different subcommittees that can be formed.
Whether you select ABC, ACB, BAC, BCA, CAB, or CBA, you still have the same 3 people
on the subcommittee. You can form the subcommittee in 210 different ways, but
each group of the same three people gets selected six times, in different ways.
So there are only (210/6) = 35 possible different subcommittees.
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