Question

A bag contains 3 white, 5 red and 7 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:

• A. 3/22
• B. 1/22
• C. 1/91
• D. 2/91
• E. none

Answer 1

The correct option is D

2/91

Let S be the sample space.

Then, (S) = number of ways of drawing 3 balls out of 15

= ${}^{15}{C}_3$=455

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

$\therefore$ (E) = ${}^5{C}_3$ = ${}^5{C}_2$ =10

P(E) = $\frac{10}{455}$ = $\frac{2}{91}$.