# Combinatorics Urns and colored balls

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 ?

• Unless you have a typo, then it's 0, as there will be 6 balls left after two draws. – Stefan4024 Oct 2 '16 at 9:54
• @Stefan4024 by latter they mean the second sample – Mike Harb Oct 2 '16 at 10:05

What is the probability that a sample of $8$ from the $20$ balls contains $4$ from the $10$ blue, $1$ from the $5$ yellow, and $3$ from the $5$ red balls?