karim.nazmy wrote: My approach is as follows:
There is a total of 9C2 combinations which are 36. To get 2 of the same color, there are 2 green combinations, 1 red and 1 yellow. Therefore, answer would be (2+1+1)/36 = 4/36= 2/9 which is incorrect as the answer here is C.

Your math doesn't quite work here. There aren't simply 2 green combinations when you have 4 balls. You need to consider every combination: green1+green2, green1+green3, green1+green4, etc.

In fact, for 4C2, there are 4!/((2!)(2!)) = 6 ways of choosing 2 of the 4 green balls. Then there are 3 ways to choose 2 out of 3 red balls: 3!/((2!)(1!)). Then there is, as you said, only 1 way to choose both yellow balls. So, there are 6 + 3 + 1 = 10 total ways of choosing 2 of the same color out of 36 total ways of choosing 2 balls of any color. 10/36 = 5/18.

The answer is C.