Thread: 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.

You must assume that each of x, y, & z is at least 2.
is the number of ways of choosing two reds marbles.
The total number of ways of choosing six marbles is without replacement.
So, .

Now you try the next one.