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,
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