# Thread: Help with choosing subsets question

1. ## Help with choosing subsets question

Greetings,

I am currently struggling on this question:

"A team has to be selected in the following way:
- 5 players
- at least 2 men and at least 2 women
- there are 12 men and 7 women"

i) How many ways can the team be selected?

I think this is just C(12,2)*C(7,2)*C(15,1)

ii) The team must now also include 3 players of height greater than 7ft.
5 males and 1 female have height satisfying this.
How many ways can we pick this?

My method so far is:

1) Pick 2 males out of 5 who are tall enough, 1 female who is tall enough, pick another female so we have min. amount of males and females, and 15 choices for the last team member. So: C(5,2)*C(1,1)*C(6,1)*C(15,1).

2) Pick 3 males out of 5 who are tall enough, 2 females and 15 choices for last team member: C(5,3)*C(7,2)*C(15,1)

Add 1) + 2) which gives us the total number of ways. Is this correct? I am unsure...it seems to give a very large number!

Thanks for any help,

combinatorixxx

2. ## Re: Help with choosing subsets question

Originally Posted by combinatorixxx
[B]"A team has to be selected in the following way:
- 5 players
- at least 2 men and at least 2 women
- there are 12 men and 7 women"
i) How many ways can the team be selected?
Answer: $\displaystyle \dbinom{12}{2}\dbinom{7}{3}+\dbinom{12}{3}\dbinom{ 7}{2}$.
WHY?

3. ## Re: Help with choosing subsets question

Originally Posted by Plato
Answer: $\displaystyle \dbinom{12}{2}\dbinom{7}{3}+\dbinom{12}{3}\dbinom{ 7}{2}$.
WHY?
We can choose in two ways - 2 males and 3 females, or 3 males and 2 females.

Hmm it makes sense now but I find it difficult to think in the correct way.

So for the second part, would we have:

2 tall males, 1 tall female, 2 females
2 tall males, 1 tall female, 1 female, 1 male
3 tall males, 2 females

$\displaystyle \dbinom{5}{2}\dbinom{1}{1}\dbinom{6}{2}+\dbinom{5} {2}\dbinom{1}{1}\dbinom{6}{1}\dbinom{10}{1} + \dbinom{5}{3}\dbinom{7}{2}$

4. ## Re: Help with choosing subsets question

Hi friends, even I not good enough in solving such problem but I enjoy lot by seeing you guys solving such problems of math.