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# Choosing subsets

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1. 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(12,3)*C(7,3) + C(12,3)*C(7,2)

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:

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

(5,2)*(1,1)*(6,2) + (5,2)*(1,1)*(6,1)*(10,1) + (5,3)*(7,2)

Thanks for any help,

combinatorixxx
2. You can't use binomials because you're choosing people without replacement - you need to use the hypergeometric distribution instead.
3. (Original post by mmmpie)
You can't use binomials because you're choosing people without replacement - you need to use the hypergeometric distribution instead.
Are you sure?

We don't study any distributions in this course; it's a maths module not stats.

I'm pretty sure we're meant to use binomials.
4. (Original post by combinatorix)
Are you sure?

We don't study any distributions in this course; it's a maths module not stats.

I'm pretty sure we're meant to use binomials.
No, thinking about it it's just a choose. You're right, sorry. I'm at the end of an all nighter and really shouldn't be trying to answer questions
5. I think you need to be careful about the following two cases:

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

In particular, the scenario "2 tall males, 1 tall female, 1 female, 1 tall male" seems to be counted under both categories.

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