Q. I have five 10-rupee notes, three 20-rupee notes, and two 50-rupee notes in my wallet. If three notes were taken out randomly and simultaneously, what is the probability that at least 90 rupees were taken out?

A. 1/20

B. 7/60

C. 1/15

D. 11/60

E. 3/20

## EXPLANATION

B

The total number of ways of selecting 3 notes from the :

five 10-rupee notes, three 20-rupee notes, and two 50-rupee notes = 10 notes in total.

10C_{3} = 120

The possibilities for the value of the three notes combined is at least 90 :

Rs 50 + Rs 20 + Rs 20 : The possibilities for this selection is :

2C_{1} x 3C_{2} Selection of one Rs 50 note from the two and selection of 2 Rs 20 notes from the three.

Rs 50 + Rs 50 + Rs 10 :

(2C_{2}) x (5C_{1}) : Selection of two Rs 50 notes from the two and selection of 1 Rs 10 notes from the five.

Rs 50 + Rs 50 + Rs 20 :

(2C_{2}) x (3C_{1}) : Selection of two Rs 50 notes from the two and selection of 1 Rs 20 notes from the three.

A total of 6+5+3 = 14 possibilties

The probability is 14/120 = 7/60

## Leave a Reply