In a bucket, there are five different colors of balls, two of each color, making 10 in total. If you pick three balls at random without replacement, what is the probability that you pick a different colored ball each time? What is the probability that you only pick two different colored balls?
I just made up a simple random scenario that demonstrates the principle/type of problem that I am trying to figure out. With the skills I acquired in pre-calculus, I would be able to solve this if it was with replacement, not without replacement. Also having several unique colors, but identical balls within each color group adds an extra layer of complexity that confuses me. What is the process to solve the problem? And, if I was to increase the number of colors, number of balls per color, or the number of times a ball is picked, could the same formula/process still be applied?