1. The problem statement, all variables and given/known data You are given a jar with 9 balls in it. 4 of which are red, 3 are green, and 2 are blue. The 9 balls are taken out of the jar one by one. What are the odds that the first 3 balls have 3 different colors? What are the odds that the last 3 ball have 3 different colors? What are the odds the the first, the third, and the seventh balls have 3 different colors? 2. Relevant equations Will be shown in the solution attempt. 3. The attempt at a solution I think I managed to solve the first question, but I would appreciate your remarks, if you have any. I am looking for an elegant way to solve the second and the third questions. [(4*3*2)*3!*6!]/9! Explanation: We have 4 options of choosing red ball, 3 of green, and 2 of blue, we multiply by 3! as the order matters. We then multiply by 6! options of taking out the next 6 available balls. We finish by dividing by 9! which is total number of options of taking out the 9 balls.