Question

A bag contains 6 white, 7 red and 5 black balls. If 3 balls are drawn from the bag at random, then the probability that all of them are white is

• A. $\frac { 20 } { 204 }$
• B. $\frac { 5 } { 204 }$
• C. $\frac { 1 } { 3 }$
• D. None of these

Answer 1

Answer: (B)

$\frac { 5 } { 204 }$

Answer 2

3 ball can be drawn in ${ } ^ { 18 } C _ { 3 }$ ways

Favourable cases $= { } ^ { 6 } C _ { 3 }$

$\therefore$ Required probability $= \frac { { } ^ { 6 } C _ { 3 } } { { } ^ { 18 } C _ { 3 } } = \frac { 6 \times 5 \times 4 } { 18 \times 17 \times 16 } = \frac { 5 } { 204 }$