Question

there are 5 men and 8 women available for a 5 person committee. Of the committee must have at least one man and one woman, how many possible committees are there?

Answer 1

Since the committee must have at least 1 man and one woman the possibilities are

1 Men and 4 Women
2 Men and 3 Women
3 Men and 2 Women
4 Men and 1 Women

Right?

Answer 2

This is found using nCr=nPr/r!?

Answer 3

This is combinatorial because order/position/rank does not matter.
so its 5C1 for men and 8C1 for women then you multiply the two answers i.e
5C1 * 8C1.

Answer 4

?

Answer 5

Actually, @barkbark, did you figure out how to compute the correct result yet?

Answer 6

@Hero Nope, thought that was correct but still am confused

Answer 7

Since the committee must have at least 1 man and one woman the possibilities are

1 Men and 4 Women
2 Men and 3 Women
3 Men and 2 Women
4 Men and 1 Women

In other words, for example since 5 men and 8 women are available then

The number of possibilities for 1 Men and 4 Women can be computed by

5C1*8C4

The number of possibilities for 2 Men and 3 Women can be computed by
5C2*8C3

And so on.

After finding the possibilities for each case, add them up to find the total number of possibilities.

Answer 8

hero im a fan lol

Answer 9

Oh thank you I see now.

Answer 10

You're welcome

Answer 11

Hero, your answer may not be right. I think you shouldn't add

Answer 12

Now I am confused....the textbook has an example similar to what @Myopeness is saying, Confused is 40 correct?

Answer 13

Yes, you are confused. I don't know how much more I can do to help you except to tell you to read through what I have explained again and try to understand. At what point did you get confused concerning my explanation?

Answer 14

@Hero I was confused by the two conflicting answers/methods given. I obtained 640 not 40 for the answer using what you explained is that correct?

Answer 15

Yes, the method that I explained is correct. I believe what @MyOpenNess explained to you was only an example. That's why he wrote i.e.

Answer 16

@Hero Thank you again! Is it based upon the wording in the question?
i.e --->The chorus of a play has 17 females and 13 males.
The director wishes to meet with 6 of them to discuss the upcoming production.
How many selections are possible if the group consists of three females and three males?
So if I calculate
17C3*13C3 = 194 480 that is not the full answer?

Answer 17

That looks right. It would be different calculation if they added "at least" somewhere in there.

Answer 18

That's the difference between this question and the previous one.

Answer 19

Ok thank you greatly! That is why I was confused. And the fact that I am not very bright apparently.

Answer 20

You figured out the answer to the question so you're definitely on the right track. Just because every now and again you have to ask for help, that doesn't mean you aren't bright. Sometimes teachers/books do not explain every concept with the best possible clarity. Also sometimes mistakes are made. Unclarity and mistakes made while explaining concepts can lead to confusion. When concepts are unclear the first time you are introduced to them, it's always a great idea to get a second opinion.