Question

An urn contains 9 balls two of which are red, three blue and four black. Three balls are drawn at random. The probability that they are of the same colour is

• A. $\frac{5}{84}$
• B. $\frac{3}{9}$
• C. $\frac{3}{7}$
• D. $\frac{7}{17}$

Answer 1

The correct option is A

$\frac{5}{84}$

Three balls can be drawn randomly from nine balls in ${}^9{C}_3=84$ ways.

Three balls cannot be red as there are only two red balls.

Three balls of the same colour can be drawn in the following ways :

3 blue out of a total of 3 blue balls.

The probability for which is $\frac{{}^3{C}_3}{84}=\frac{1}{84}$

3 black out of a total of 4 black balls.

The probability for which is $\frac{{}^4{C}_3}{84}=\frac{4}{84}$

Hence, required probabililty $=\frac{1}{84}+\frac{4}{84}$

$=\frac{5}{84}$