A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random

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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:

Options:

A . 1 22

B . 3 22

C . 2 91

D . 2 77

Answer: Option C

Let S be the sample space.

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

Let E = event of getting all the 3 red balls.

n(E) = ⁵C₃ = ⁵C₂ =
(5 x 4)
= 10.
(2 x 1)

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

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