A box contains 5 green, 4 yellow and 3 white marbles. Three marbles are drawn at random. What is the probability that all they are not of the same colour?

Solution (By Examveda Team)

Let balls are GGGGG, YYYY and WWW.

So, we could solve this question in 2 different ways:

The question can be solve by consedring the two senarios:

1) We can calculate the things that we want in above case senarios is not the same colour.

2. The things we don't want. In this senario we can calculate the answer (1 - we don't want ).

So, the scenarios we don't want are:

Probability of Getting a Green ball from the box = (5/12) * (4/11) * (3/10) = 60/1320

Probability of Getting Yellow ball = (4/12) * (3/11) * (2/10) = 24/1320

Probability of Getting White Ball = (3/12) * (2/11) * (1/10) = 6 /1320

So, Probability of getting Green or Yellow or White ball = (60/1320) + (24/1320) + (6/1320) = 9/132 = 3/44.

**"Not of the same colour" means that "not all 3 can be the same colour". So, you need to take into account the scenarios in which you have 2 of 1 colour and 1 of a second colour.