16. A student has to sell 2 books from a collection of 6 math, 7 science, and 4 economics books. How many choices are possible if

(b) the books are to be on different subjects?

So for the first pass one can choose one book out of one of the three piles so, $\displaystyle \binom{6}{1}+\binom{7}{1}+\binom{4}{1}=17$.

For the second pass one can only choose a book from a pool that wasn't selected from the first pool. Leaving 3 options;

1. If you selected from $\displaystyle \binom{6}{1}$ then $\displaystyle \binom{7}{1}+\binom{4}{1}=11$

2. If you selected from $\displaystyle \binom{7}{1}$ then $\displaystyle \binom{6}{1}+\binom{4}{1}=10$

3. If you selected from $\displaystyle \binom{4}{1}$ then $\displaystyle \binom{6}{1}+\binom{7}{1}=13$

I'm not entirely sure what I've done wrong here. I think I should just be able to add everything from pass one and pass two to get the correct answer but the listed answer is 94 and $\displaystyle 51\neq94$

Could someone clue me into what I'm doing wrong here?