A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is-

Question: A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is-

Solution:
Let, S be the sample space

Then,
n(S) = number of ways of drawing 3 balls out of 15
= ¹⁵C₃
= (15 × 14 × 13)/(3 × 2 × 1)
= 455

Let, E = event of getting all the 3 red balls
∴ n(E) = ⁵C₃
= ⁵C₂
= (5 × 4)/(2 × 1)
= 10

∴ P(E) = n(E)/n(S)
= 10/455
= 2/91