# A bag contains 4 white, 5 red and 6 blue balls.

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:

## Answer/Solution

2/91

### Steps/Work

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)/(2 x 1)= 10.

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

Ans:D

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)/(2 x 1)= 10.

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

Ans:D