Sorry if this has been asked before, i can't get my head around how to take into account that the order of the balls being drawn is not important.
2026-04-12 21:38:21.1776029901
The probability of choosing a particular color combination of balls after five draws
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This is a multinomial distribution.
The probability of drawing the balls in a specific order is: $(6/15)^3(4/15)(5/15)$
However, there are $5!/3!$ distinct orders to draw 3 blue, 1 red, and 1 white balls.
Thus the answer is: $$\begin{align}\mathsf P(B=3,R=1,W=1) & = \dbinom{5}{3,1,1}(\tfrac 6{15})^3(\tfrac 4{15})(\tfrac 5{15}) \\[1ex] & = \frac{128}{1125} \\[1ex] &= 0.113\overline{7}\end{align}$$