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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:

1 22
3 22
2 91
2 77

Correct Answer: 2 91

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

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