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:

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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:

[A].

1
22

[B].

3
22

[C].

2
91

[D].

2
77

Answer: Option C

Explanation:

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