What is his expectation? 
A man draws 3 balls from a jug containing 5 white balls & 7 black balls. He gets Rs. 20 for each white ball & Rs. 10 for each black ball. What is his expectation?
$\\ $ a) $Rs. 21.25\ \quad $ b) $Rs. 42.50 \quad$ c) $Rs. 31.25\ \quad $ d) $Rs. 45.21\ $

My attempt:
Probability of drawing 2 white balls & 1 black ball out of 12 balls
$$=\frac{\binom{5}{2}\cdot \binom{7}{1}}{\binom{12}{3}}=\frac{7}{22}$$
Probability of drawing 1 white ball & 2 black balls out of 12 balls
$$=\frac{\binom{5}{1}\cdot \binom{7}{2}}{\binom{12}{3}}=\frac{21}{44}$$
as there are two different ways of drawing three balls hence the total expectation
$$=(2\times20+10)\frac{7}{22}+(20+2\times10)\frac{21}{44}=Rs. 35$$
My answer is not matching with any option. Can somebody please help me where I am wrong? Thanks.

You missed the options of taking three white balls with probability: $$\frac{\binom{5}{3}}{\binom{12}{3}}= \frac{10}{220}=\frac{1}{22}$$ and taking three black balls with probability: $$\frac{\binom{7}{3}}{\binom{12}{3}}= \frac{35}{220}=\frac{7}{44}$$
So, you missed up a total of: ??
