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?

A. $$\frac{{1}}{{455}}$$

B. $$\frac{{2}}{{455}}$$

C. $$\frac{{1}}{{91}}$$

D. $$\frac{{4}}{{455}}$$

Answer: Option A

Solution(By Examveda Team)

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 = $$\frac{{{}^3{C_3}}}{{{}^{15}{C_3}}}$$
$$\eqalign{ & = \frac{{1 \times 3 \times 2 \times 1}}{{15 \times 14 \times 13}} \cr & = \frac{6}{{2730}} \cr & = \frac{1}{{455}} \cr} $$