A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?

Answer: Option A

Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = $$\frac{{}^3{C}_3}{{}^{15}{C}_3}$$
$$\begin{array}{rl}& =\frac{1\times 3\times 2\times 1}{15\times 14\times 13}\\ & =\frac{6}{2730}\\ & =\frac{1}{455}\end{array}$$