If a bag contains three blue, four green and five red identical balls, what is the probability that if four balls are picked at random, one after the other, without replacement, that the first two are of the same colour and the last two are of different colours?

This combines the probability that:

2 blue balls are picked followed by 1 green and 1 red,
2 blue balls are picked followed by 1 red and 1 green,
2 green balls are picked followed by 1 blue and 1 red,
2 green balls are picked followed by 1 red and 1 blue,
2 red balls are picked followed by 1 blue and 1 green,
2 red balls are picked followed by 1 green and 1 blue.

Can you find each of them? Then add all of them together.