MHB What is the Probability of Grouping All Red Marbles Together?

[sscs]

I need help starting the following problem.

There are (36) marbles in a bag-(32) are green and (4) are red. The marbles are to be divided equally into (3) groups of (12). What is the probability that one of the groups will contain all of the (4) red marbles?

 

[MarkFL]

Re: Basic Probability

I would look at this as a partitioning problem. How many ways can we partition 4 objects into 3 groups (2 partitions with 5 potential positions), and how many of those ways have all four objects in one group?

 

[eddybob123]

Re: Basic Probability

Or another way to think of it is you're "choosing" 12 marbles out of a bag at random. There are a few separate cases you have to consider:

Case #1: Choosing all 4 red marbles out of the bag at once.
Case #2a: Not choosing any red marbles out of the bag, and choosing another 12 marbles, with all 4 of the red marbles in that group.
Case #2b: Not choosing any red marbles out of the bag, then choosing another 12 marbles and not getting any red marbles out of that either.

Find the probabilities of each of these cases and then add them.