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?

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