From a bag contains 5 red balls and 3 black balls. A man drawn two balls at random. What is the probability of these balls not of the same colour

Total number of balls $=5+3=8$

Number of ways of drawing two balls from 8 these balls $={}^8{\text{C}}_2$

For the balls drawn to be not of the same colour i.e., one must be red and the other must be black.

Probability $=\frac{{}^5{\text{C}}_1\times {}^3{\text{C}}_1}{{}^8{\text{C}}_2}=\frac{15}{28}$