Chances of picking a basketball team

[torquerotates]

Homework Statement

A 3 person basketball team consists of a guard, a forward and a center. If a person is chosen randomly from each of 3 different such teams, what is the probability of selecting a complete team?

Homework Equations

The Attempt at a Solution

Well my reasoning is that for the guard on the team, I have to pick from one of the teams. So looking at one of the teams, i can pick out of 3 to be the guard. Then i have to look at the next team of which i can only pick out of 2 to be the forward and finally the last team only offers me one choice. So its (3+2+1)/9=2/3

but the answer in the back of the book gives 2/9. something's wrong.

 

[lurflurf]

Oh badness. You have added when you should have multiplied. That should be
(3/3)*(2/3)*(1/3)=2/9
not
(3/3)+(2/3)+(1/3)=2/3

 

[Dick]

You haven't even just added. Your reasoning is completely correct. 3 choices from the first team, 2 from the second and 1 from the last. That's 3*2*1 choices that give you a complete team. How many possible choices of three regardless of whether they form a team?

 

[torquerotates]

How many possible choices of three regardless of whether they form a team?

well it would be, going by your reasoning, 3*3*3=9

But I still don't understand why you multiply instead of add.

 

[Dick]

3*3*3=27. Come on.