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

Let S be the sample space.
Then n(S) = no of ways of drawing 2 balls out of (6 + 4) = ¹⁰C₂
= (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
= (6 × 5)/(2 × 1) + (4 × 3)/(2 × 1)
= 15 + 6
= 21
Therefore,
P(E) = n(E)/n(S)
= 21/45
= 7/15