An urn contains 10 blue balls , 5 yellow balls and 5 red balls. Six balls are drawn from the urn and discarded, their color unnoticed. A second sample of 8 balls is then drawn without replacement. What is the probability that the latter contains 4 blue balls, 1 yellow ball and 3 red balls.
The question is fairly simple to understand but is there any other way to solve it without counting all the different possibilities of the first sample ?