Question

A bag contains 12 two rupee coins, 7 one rupee coins and 4 fifty paise coins. If three coins are selected at random, then the probability that the sum of the values of the three coins is not an integral multiple of a rupee is

• A. $ \frac{4 \binom{12}{2} \binom{7}{2} + \binom{12}{1} \binom{7}{1} \binom{4}{2} + 3 (\binom{12}{1} + \binom{7}{1})}{\binom{23}{3}} $
• B. $ \frac{4 \binom{12}{1} \binom{7}{1} + \binom{12}{2} + \binom{7}{2} + \binom{4}{2} + 3 \binom{4}{3}}{\binom{23}{3}} $
• C. $ \frac{4 \binom{12}{2} \binom{7}{1} + \binom{12}{1} \binom{7}{2} + 3 (\binom{12}{1} \binom{7}{2})}{\binom{23}{3}} $
• D. $ \frac{4 \binom{12}{3} + 3 \binom{12}{1} + \binom{7}{1}}{\binom{23}{3}} $

Hint:

The sum of the values is not an integer multiple of a rupee if and only if there is an odd number of fifty paise coins selected.

Answer 1

The Correct Option is B

N/A