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

Question

Compute the probability that all of the balls in the sample are the same color. (Round your answer to four decimal places.)

Answer 1

you want the probability that all 4 balls are either red or white or blue

use n!/r!(n-r)! for each color

(8!/4!4! + 8!/4!4! + 8!/4!4!)/(24!/4!20!)  (the denominator is how many ways you can pick 4 balls from a total of 24 balls and "or" implies addition)

(8*7*6*5)/(4*3*2) + (8*7*6*5)/(4*3*2) + (8*7*6*5)/(4*3*2) gives the numerator

(24*23*22*21)/(4*3*2) gives the denominator

70+70+70=210 is the numerator

23*22*21=10,626 is the denominator

the probability is 210/10,626=105/5313

105/5313=35/1771

35/1771=5/253

5/253=0.0197628=0.0198 to 4 decimal places