# Math Help - Combinatorics Question

1. ## Combinatorics Question

I have two questions about probabilities when choosing things from a set.

Assume you have a bag of x red marbles, y blue marbles, and z green marbles.

1. If you choose 6 marbles from the bag, without replacement, what is the probability that you get exactly 2 of each type of marble?

2. If you choose 6 marbles from the bag, with replacement, what is the probability that you get exactly 2 of each type of marble?

I'm not really sure how to go about solving these.

Thanks for any help.

2. You must assume that each of x, y, & z is at least 2.
${ x \choose 2} = \frac {x!}{(x-2)!(2!)}$ is the number of ways of choosing two reds marbles.
The total number of ways of choosing six marbles is ${x+y+z \choose 6}$ without replacement.
So, $\frac {{ x \choose 2}{ y \choose 2}{ z \choose 2}}{{x+y+z \choose 6}}$.

Now you try the next one.