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 = 455

Let E = event of getting all the 3 red balls.
n(E) = ⁵C₃ = 10

P(E) = n(E)/n(S) = 10/455 = 2/91