Hey guys, I'm currently working on a fun project and I need some help. Imagine if you will you have a bag of balls (lawl bag of balls) and in that bag of balls are 3 red balls 4 green ball 2 blue balls(LAWL) and 1 yellow balls. Also in this bag there are 55 other balls that can be any other color other then the once already mentioned. To keep things simple lets say the other 55 balls are black.

What I want to figure out is what is if I pick 7 balls at random what is the probability that I will pick at least one of each of the non black balls?

I was thinking I'd obviously have to use Multivariate Hyper-geometric Distribution. But then I realized that I think that might not work since Multivariate Hyper-geometric Distribution is usually used for determining an exact amount as oppose to an "at least" certain amount.

If we wanted to calculate the probability of picking exactly one of each and we were only picking 5 I think the equation would look like this:

NOTE: the c is short for choose which is used to represent a combination where order doesn't matter.



I was thinking to solve my question I could modify it to look like so:


My reasoning behind is this: as long as one of each color is present we don't care what the other 3 picks are. Thinking about it it seems wrong to just add 6 to the last combination. Let me know what you guys think.[i][/i]