An opaque bag contains 10 green counters, and 20 red ones. One counter is drawn at random and not replaced: green scores one, red scores zero. Five counters are drawn.
Find the probability of scoring 0, 1, 2, 3, 4, 5 points.
The Attempt at a Solution
I found it pretty straighforward to work out with replacement, as it is just the simple binomial probability. But when the counters aren't replaced, surely the order counts, so i tried replacing nCr with nPr though this gave me the completely wrong answer. i know this resembles the lottery problem, but i don't understand what to do when there are only 2 distinguishable groups.