Suppose a basket contains $B$ blue balls and $R$ red balls. Then, suppose I pick $N$ balls from the basket. What is the probability that I get
- At least $b$ blue ones and $r$ red ones
- At least $b$ blue ones and exactly $r$ red ones
- Exactly $b$ blue ones and exactly $r$ red ones
How does the solution differ if I put the balls back or don't?
I suppose this is a very basic problem in statistics so I attempted to cover a range of related problems here. I suppose I should know about permutations and combinations for solving this. (This is not a homework, I'm studying stats for fun.) What I am trying to learn here is how to solve any similar kind of problem.