A bag contains 6 white and 4 black balls. Two balls are drawn at random. Find the probability that they are of same colour.

Answer: Option D

Number of ways two balls can be drawn from 10 balls (6 white +4 blacks)
$$={}^{10}{C}_2=\frac{10\times 9}{2\times 1}=45$$
n(E) = Number of ways of drawing 2 balls from 6 white balls or 2 balls from 4 black balls
$$\begin{array}{rl}& ={}^6{C}_2+{}^4{C}_2=21\\ & \text{P}\left(\text{E}\right)=\frac{21}{45}=\frac{7}{15}\end{array}$$