A bag contains 12 two rupee coins, 7 one rupee coins and 4 half rupee coins. If 3 coins are selected at random, then the probability that the sum of the 3 coins is maximum is 

The random experiment is " picking 3 coins at a time from the bag of coins" 

Let S be the sample space, $n\left(S\right)={\left(12+7+4\right)}_{C_3}={23}_{C_3}$

Let $E$ be the event of getting maximum sum on the coins, it means 3 coins must be all three two rupee coins

$n\left(E\right)={12}_{C_3}$

Hence, the probability is $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\boxed{\frac{{12}_{C_3}}{{23}_{C_3}}}$