Question

There are total $18$ balls in a bag. Out of them, $6$ are red in colour, $4$ are green in colour and $8$ are blue in colour. If Vishal picks three balls randomly from the bag, then what is the probability that all the three balls are not of the same colour?

• A. $\frac{46}{51}$
• B. $\frac{49}{51}$
• C. $\frac{43}{51}$
• D. $\frac{41}{51}$

Answer 1

The correct option is A $\frac{46}{51}$

Number of ways in which Vishal can pick three balls out of $18$ balls $={}^{18}{C}_3$
Number of ways of picking $3$ balls of same colour $={}^6{C}_3+{}^4{C}_3+{}^8{C}_3=20+4+56=80$
Probability of picking three balls of same colour $=\frac{80}{{}^{18}{C}_3}=\frac{5}{51}$
Required probability $=1-$ probability of picking three balls of same colour
$=1-\frac{5}{51}=\frac{46}{51}$