**A. \(\frac{2}{91}\)**

B. \(\frac{3}{21}\)

C. \(\frac{12}{31}\)

D. \(\frac{1}{13}\)

**Solution:**

Let S be the sample space.

Then, n(S) = number of ways of drawing 3 balls out of 15

\left. \begin{array} { l } { \quad = ^ { 15 } C _ { 3 } } \\ { = \frac { ( 15 \times 14 \times 13 ) } { ( 3 \times 2 \times 1 ) } } \\ { = 455 } \\ { \text { Let } E = \text { event of getting all the } 3 \text { red balls. } } \\ { \therefore \quad n ( E ) = ^ { 5 } C _ { 3 } = ^ { 5 } C _ { 2 } = \frac { ( 5 \times 4 ) } { ( 2 \times 1 ) } = 10 } \\ { \therefore P ( E ) = \frac { n ( E ) } { n ( S ) } = \frac { 10 } { 455 } = \frac { 2 } { 91 } } \end{array}