probability – Clear my doubt regarding this probabililty concept.

A bag contains 2 red and 3 green balls. 2 balls are draw at random. Find the probability that the ball is red and green.What is the correct solution to the problem.

Solution 1- 2/5 * 3/4 = 3/10 i.e probability of getting red multiplied by probability of getting green from the remaining balls.

Solution 2- 2C1 * 3C1/ 5C2 = 2*3/10=3/5 Using combinations.

I cant understand the difference between the two. In many books answer is given as solution 1, simple way. Whereas is some others for the same kind of questions, they are doing using combinations.
In which type of questions can we use the simple method and when we have to take combinations for finding the probability.