When should we use combination and when should we use ratios to determine probability?

When should we use combination and when should we use ratios to determine
probability?

So I have this question:
a box contains 8 balls
2 red and 6 black, 2 balls are drawn in succession and with replacement
the answer is:
(2/8)(2/8) + (6/8)(6/8)
now, i have another question:
3 balls are drawn in succession we have 3 white 4 red and 5 green balls,
we win 1 dollar when we get a white ball and lose 1 dollar when we get a
red ball and 0 if we get a green ball.
what's the probability of getting 0 dollars?
I did this thinking the problem was of the same type:
we need 3 green or 1 white, 1 red and 1 green without replacement
(5/12)(4/11)(3/10) + (3/12)(4/11)(5/10)
however, this is false.
notice how we could word the question almost the same way.