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.
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 x 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) x (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) x (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 14/120 = 7/60
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