I tried to solve using combinatorics but I was wrong - answer below.
I thought there is 16 balls in total and if we select three from 16, we have 16!/3!13! ways to choose three balls.
BGR is one of each and there is 6 ways of organising
we have 1C7x 1C5 x 1C4 x 6 / number of ways to choose three balls
so we have 7 x 5 x 4 x 6 / 16 x 15 x 14 x 3 x 2
Simplifying the sixes 7 x 5 x 4 / 16 x 15 x 14
simplifying 7 and 14 1 x 5 x 4 / 16 x 15 x 2
Simplifying 5 and 15 1 x 1 x 4 / 16 x 3 x 2
Simplifying 4, 16 1 x 1 x 1 / 4 x 3 x 2
Answer would be 1/24
However
Using simple probabilities
6x 7/16 x 5/15 x 4/14 = 1/4
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