A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:

Answer: Option C

Let S be the sample space
Then, n(S) = number of ways of drawing 3 balls out of 15
$$\begin{array}{rl}& ={}^{15}{C}_3\\ & =\frac{15\times 14\times 13}{3\times 2\times 1}\\ & =455\end{array}$$
Let E = event of getting all the 3 red balls
$$\begin{array}{rl}& \therefore n\left(E\right)={}^5{C}_3={}^5{C}_2\\ & =\frac{5\times 4}{2\times 1}=10\\ & \therefore P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}\\ & =\frac{10}{455}\\ & =\frac{2}{91}\end{array}$$