For the following questions there is a club consisting of six distinct men and seven distinct women.(adsbygoogle = window.adsbygoogle || []).push({});

1. In how many ways can we select a committee of three men and four women?

There are C(6,3) ways to select the men and C(7,4) ways to select the woman. For each combination of the men there C(7,4) combinations for woman so the answer is 20*35. Does anyone see a problem here?

2. In how many ways can we select a committee of four persons that has at least one woman?

I look at this as a Total minus the bad leaves the good. The total ways of selecting a committee of four people out of 13 is C(13,4) and since there are six men there will be C(6,4) combinations that are all men. So the answer is C(13,4)-C(6,4).

3. In how many ways can we select a committee of four persons that has persons of both sexes?

Well there are C(13,4) total ways to select this committee and at least some of them are all female or all male. Well there are C(7,4) that are all female and there are C(6,4) that are all male. Once again total minus bad is good so we have C(13,4)-[C(7,4)+C(6,4)].

Thanks

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# Couple of quick combination questions

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