A bag contains 6 white and 4 black balls .2 balls are drawn at random. Find the probability that they are of same colour.

Let S be the sample space

Then n(S) = no of ways of drawing 2 balls out of (6+4) = $10C2$ 10 = $\frac{10*9}{2*1}$ =45

Let E = event of getting both balls of same colour

Then,n(E) = no of ways (2 balls out of six) or (2 balls out of 4)

                = $6C2+4C2$ =  $\frac{6*5}{2*1}+\frac{4*3}{2*1}$= 15+6 = 21

Therefore, P(E) = n(E)/n(S) = 21/45 = 7/15