Two balls are drawn at random from a bag containing 2 white, 3 red, 5 green and 4 black balls, one by one without, replacement. Find the probability that both the balls are of different colours.
given: 2 white, 3 red, 5 green, 4 black
formula: 
two balls are drawn one by one, we have to find the probability that they are of different colours
total possible outcomes are 14C2
therefore n(S)= 14C2=91
let E be the event that all balls are of same colour
E= {WW, RR, GG, BB}
n(E)= 2C2+3C2+5C2+4C2=20
probability of occurrence is
Therefore, the probability of non-occurrence of the event (all balls are different) is
28