Finding combinations in an urn model

[hashi]

Hi, this is my first post on this forum, i hope you can help. I seem to have confused my self with the following problem.

Given an urn with R red balls and B blue balls and R+B = N, and N is always even. You remove the two balls at a time from the urn until it is empty - the without replacement case.

Therefore,
a) what is the probability of some i (r, b) pairs. for example, given R=4 and B=8, what probability of the set containing 2 {r, b} pairs, i.e {r, b}, {r, b}, {r, ,r}, {b,b}, {b,b}, {b,b}

b) what is the probability of each set that contains at least one {r,b} pair.

thanks for your help.

 

[Valkarie]

The probability of getting a set containing two {r, b} pairs is:P = (R/N) * (B/N-1) * (R/N-2) * (B/N-3)For the second question, the probability of getting a set containing at least one {r,b} pair is:P = 1 - [ (R/N) * (R/N-1) + (B/N) * (B/N-1) ]