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Question:

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?

Explanation:

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.

10C₃​ ​​​​​​= 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:

2C₁ . 3C₂. 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:

(2C₂) . (5C₁) : 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:

(2C₂) . (3C₁): 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.