Question

a box contains 4 black balls, 3 red balls and 5 green balls. 2 balls are drawn from the box at random. what is the probability that both the balls are of the same colour?

Answer 1

Let us assume that all balls are unique.  

There are a total of 9 balls.  

Total ways = 3 balls can be chosen in 9C3 ways = 9!/(6!3!) = 9*8*7/3*2*1 = 84

Favorable ways = 1 Red ball, 1 Black ball, and 1 Blue Ball = 2*3*4 = 24

Required probability = Favorable ways / Total ways = 24/84 = 2/7