# Math Help - ways to choose a soccer team

1. ## 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?

2. 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?

3. wouldnt that also disclude when just bob or just joe is on it?

4. Hello,

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