Hi all. I have stumbled across this website by simply googling maths forums - boy am I glad this site is here.

I have a recurring problem with a series of projects I am working on, and this problem is, unfortunately for me, probability related. I studied data mining, PDE's, and calculus, and only completed the very basic level stats subjects at Uni, so I'm lost when probability questions get more than a little complex.

The type of problem I have is this:

Code:

There are p holes
There are p balls, q of which are red, r of which aren't red
Of the p holes, s of those holes are 'special'
Of all the possible distributions of the p balls amongst the p holes, what is the chance that n of the 'special' holes will hold red balls?

If that's too much to wrap your head around, here's a numerical example:

Code:

30 holes
10 red balls, 20 white balls
5 holes are 'special'
Of all possible distributions, what are the chances that:
0 special holes will contain red balls
Only 1 special hole will contain red ball
Only 2 special holes will contain red balls
.....
All 5 special holes will contain red balls

I'm totally at a loss with this sort of problem...