While the colors are distinguishable from each other, the marbles themselves are all indistinguishable. The way I thought about it is that the sample space is the number of ways you can distribute 15 marbles to 3 different color "bins." Using stars and bars, this would be $\binom{15+3-1}{15} = \binom{17}{15}$. For the ways to get 5 of each color, I would take the 15 marbles and distribute 5 to each bin. This could be done in only 1 way. Would the final probability be $\frac{1}{136} = 0.00735294117$?
A bag contains 20 red marbles, 20 green marbles and 20 blue marbles. You grab 15 marbles. the probability of getting 5 of each color
combinatoricsdiscrete mathematicsprobability
Best Answer
You only need to know the probability of getting $5$ blue marbles out of $20$, $5$ green marbles out of $20$ and $5$ red marbles out of $20$. That is simply
$$\frac{\binom{20}{5}\binom{20}{5}\binom{20}{5}}{\binom{60}{15}}=0.07005964009$$