In a box, 4 coins of ten rupees, 2 coins of five rupees, 2 coins of two rupees and 2 coins of one rupee are put. Now, three coins are taken out randomly. What is the probability that the amount drawn is 12 rupees?
Correct Answer: Option E
There are 4 coins of ten rupees, 2 coins of five rupees, 2 coins of two rupees and 2 coins of one rupee.
Total coins = 4 + 2 + 2 + 2 = 10
Total number of ways in which 3 coins can be taken out = 10C3 = 120
Amount drawn can be 12 rupees in the following cases:
i) 1 coin of ten rupees and 2 coins of 1 rupee
This can be done in 4C1 x 2C2 ways, i.e. 4 x 1 = 4 ways.
ii) 2 coins of five rupees and 1 coin of 2 rupees
This can be done in 2C2 x 2C1 ways, i.e. 1 x 2 = 2 ways.
Total number of ways in which 10 rupees can be drawn = 4 + 2 = 6.
∴ Probability of drawing 10 rupees = (Total number of ways in which 10 rupees can be drawn in three coins/ Total number of ways in which 3 coins can be drawn) = 6/120 = 1/20.
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