1. ## Number of combinations

Hi,

I have this problem that i can't get right.

A team of 5 people are selected to participate in a chess tournament.
The "team" is picked within a school class with 17 boys and 13 girls. The rules state that the team must consist of at least 2 boys and 2 girls.

In how many ways can the team be selected?

So i thought this would be as simple as:

Either 2 boys and 3 girls or 3 boys and 2 girls.

$$(17*16*15/3) * (13*12/2)*(13*12*11/3)*(17*16/2)$$

That is incorrect though...

Any ideas on how to do this?

2. Originally Posted by Jones
Hi,

I have this problem that i can't get right.

A team of 5 people are selected to participate in a chess tournament.
The "team" is picked within a school class with 17 boys and 13 girls. The rules state that the team must consist of at least 2 boys and 2 girls.

In how many ways can the team be selected?

So i thought this would be as simple as:

Either 2 boys and 3 girls or 3 boys and 2 girls.

$(17*16*15/3) * (13*12/2)*(13*12*11/3)*(17*16/2)$

That is incorrect though...

Any ideas on how to do this?
2 boys and 3 girls: ${17 \choose 2} \cdot {13 \choose 3} = \, ....$

3 boys and 2 girls: ${17 \choose 3} \cdot {13 \choose 2} = \, ....$

Now add the two numbers together.

3. Originally Posted by Jones
A team of 5 people are selected to participate in a chess tournament. The "team" is picked within a school class with 17 boys and 13 girls. The rules state that the team must consist of at least 2 boys and 2 girls.
${{17}\choose{3}}{{13}\choose{2}}+{{17}\choose{2}}{ {13}\choose{3}}$.
That choose three boys and two girls or two boys and three girls.

4. Originally Posted by Plato
${{17}\choose{3}}{{13}\choose{2}}+{{17}\choose{2}}{ {13}\choose{3}}$.
That choose three boys and two girls or two boys and three girls.
A rare event - we both get the same answer (which means I've got a combinatorial question correct for once).

5. hah, it turned out to be really easy.

Did i make a twat out of myself?