I can't find this exact question. The specific question I have is this:
If you have a bag with one red, one blue, and one green ball, the chance of picking any particular one is 1/3. Simple enough. Let's say you do it eight times in a row, though. Are the chances of picking the same color eight times in a row 1/6561, or about 0.015%? I'm not sure if you would triple that, since it could happen for any particular color, or if that's already factored in somehow. Or maybe it's both, depending on if the color matters.
The more general question is what would the formula for figuring out any particular combination of colors, e.g. three reds, three blues, and two greens, if the order of selection doesn't matter. I'd also like to see the most generic formula for any number of balls and any number of selections.