Couple of quick combination questions

[Townsend]

For the following questions there is a club consisting of six distinct men and seven distinct women.

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

 

[Gokul43201]

They all look good.

 

[Townsend]

I realize that this is off the topic but I was wondering something about textbooks. I learn best by practicing a lot. I know that comes as no surprise I am I sure that we all know that the more practice someone gets at something the better they are at something. Well when practicing math problems from certain textbooks there are only a couple of answers given in the back of the book. Why is that? I cannot think of one good reason for not giving all the answers except in a few cases. What good does working a problem do me if I will never know if I get it right or not? I have yet to have my homework assignments graded in any math class so it is not like I would be cheating. All the homework I do I do because I want to practice and learn and become a better math student. I need to know if what I am doing is producing correct answers to really make progress though. What happens when I think I understand a problem but I really don't? Unless I post the questions on here for verification I am left without ever knowing how well I understand the problems. Then comes test day and to nobodies surprise there are problems similar to the problems from the textbook that I thought I did correct, but I did not, and so I miss it.

How has this helped me in any way at all? It is not like after seeing that I missed it on the test I am all of a sudden going to learn it for all time and know it better than if I had gotten all of the problems correct.

Sorry, guess I am just a bit frustrated with text that only give answers to selected problems. Maybe there is something psychological about only giving a few answers or something but overall I think it is ineffective and very frustrating.

 

[Townsend]

They all look good.

Thanks Gokul, I really do appericate it.