Question 73

# 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?

Solution

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.

$$10_{C_3}$$

= 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  :

$$2_{C_1}\cdot3C_2$$. 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 :

$$\left(2_{C_2}\right)\cdot\left(5_{C_1}\right)$$ : 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 :

$$\left(2_{C_2}\right)\cdot\left(3C_1\right)$$ : 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 $$\frac{14}{120}$$ = 7/60.

### Video Solution

• All Quant Formulas and shortcuts PDF
• XAT previous papers with solutions PDF