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:

Explanation:-

Let S be the sample space.
Then, n(S) = number of ways of drawing 3 balls out of 15 $$\eqalign{ & = {}^{15}{C_3} \cr & = \frac{{\left( {15 \times 14 \times 13} \right)}}{{\left( {3 \times 2 \times 1} \right)}} \cr & = 455. \cr & {\text{Let}}\,{\text{E}}\,{\text{ = }}\,{\text{event}}\,{\text{of}}\,{\text{getting}}\,{\text{all}}\,{\text{the}}\,{\text{3}}\,{\text{red}}\,{\text{balls}} \cr & \therefore n\left( E \right) = {}^5{C_3} = {}^5{C_2} \cr & = \frac{{\left( {5 \times 4} \right)}}{{\left( {2 \times 1} \right)}} = 10. \cr & \therefore P\left( E \right) = \frac{{n\left( E \right)}}{{n\left( S \right)}} \cr & = \frac{{10}}{{455}} \cr & = \frac{2}{{91}}. \cr}$$