# Thread: Combinatorial Prob.

1. ## Combinatorial Prob.

Suppose that there are 7 soccer players and 6 football players on a bus. Find the probability that a group of 5 players selected at random will consist of 3 soccer players and 2 football players.

2. ## Re: Combinatorial Prob.

From soccer players $\displaystyle \binom{3}{7}$

From football players $\displaystyle \binom{2}{6}$

In total $\displaystyle \binom{5}{13}$

3. ## Re: Combinatorial Prob.

Hi,Thank you for the help! the answer is the back of the book says it is .408. Would you mind explaining it please?

4. ## Re: Combinatorial Prob.

Originally Posted by kangta27
Hi,Thank you for the help! the answer is the back of the book says it is .408. Would you mind explaining it please?
$\displaystyle \frac{\dbinom{7}{3}*\dbinom{6}{2}}{\dbinom{13}{5}} \approx 0.408$

5. ## Re: Combinatorial Prob.

Originally Posted by pickslides
From soccer players $\displaystyle \binom{3}{7}$

From football players $\displaystyle \binom{2}{6}$

In total $\displaystyle \binom{5}{13}$
Hmmm ... each of those equals zero.

6. ## Re: Combinatorial Prob.

Originally Posted by alexmahone
Hmmm ... each of those equals zero.
As you can see, I'm having one of my upside down days!