Probability Q35

35.	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