An urn contains nine red balls, nine white balls, and nine blue balls, and sample of four balls is drawn at random without replacement.

Compute the probability that all of the balls in the sample are the same color.

Question

An urn contains nine red balls, nine white balls, and nine blue balls, and sample of four balls is drawn at random without replacement.

Compute the probability that all of the balls in the sample are the same color.

anonymous · Answer

so C(27,4) would give the formula for the total samples. Which leads to the formula (27!)/4!(27-4)! = 17550 samples. 
From here I find the possible value of choosing all colors of the same type. I start by finding the possible ways of having a single color. C(9,4)= (9!)/4!(9-4)!=126
So there are 126 combinations, lets say of red. 
Since we have 3 colors, i multiple 126 by 3 = 378/17550 = .0215