# ways to choose a soccer team

• May 3rd 2008, 04:23 PM
stones44
ways to choose a soccer team
you have 18 people to choose from and you are making an 11 person soccer team....how many ways are there to choose a team so that Bob and Joe are not on the team together

there are 18 C 11 ways total and then is it 17 C 11 if bob doesnt play and then multiply it by two for if joe doesnt play

so 2(17 C 11)

is that correct?
• May 3rd 2008, 04:34 PM
Plato
Without any restrictions there are $\binom{18}{11}$ possible teams
There are $\binom{16}{9}$ possible teams that include both Bob and Joe.

Would the difference be the answer to the question?
• May 4th 2008, 07:01 AM
stones44
wouldnt that also disclude when just bob or just joe is on it?
• May 4th 2008, 07:47 AM
Moo
Hello,

Quote:

Originally Posted by stones44
wouldnt that also disclude when just bob or just joe is on it?

No, because it's only "BOTH are in the team", it's the only possibility you disclude from the whole. Thus remain the possibilities of "one of them is in the team" and "none of them is in the team".

The case where both of them are in the team is the only one we want to avoid.

I hope it helps you understand :x