I have the following trivial problem:
An urn has $6$ balls, $1$ red, $1$ blue and $4$ green. If $3$ balls are selected at random, what is the probability of them being the combination of $1$ red and $2$ green.
The problem can be trivially solved, by the following counting method:
Where number of combinations that contain only 1 red ball over the total number of combinations of size 3.
My question is that I'm trying to solve the problem using the more basic probability technique (not sure of the correct wording) I've constructed the following 2 statements:
$$Pr(1R \ 2G)=1/6\cdot3/5\cdot3/4=1/10$$ or $$Pr(1R \ 2G)=1/6\cdot(1-1/5)\cdot(1-1/4)=1/10$$
Neither of them determine the correct result. I believe I'm missing a crucial point, I would prefer hints or suggestions rather than a complete answer if possible.