In a shelf there are 6 Math books, 8 Programming books and 10 Physics books.
The first question is: In how many ways can one choose 3 books, one book for each subject?
The second question: In how many ways can one choose a book regardless of subject?
For the second I get 24, because in total there are 24 books
Best Answer
If you choose one for each type, you have $6$ choices for the first type, $8$ for the second and $10$ for the third one. Therefore, the answer is $6\times8\times10=480$.
Otherwise, you want to choose $3$ books among $24$. So, you have $\binom{24}3$ ways of doing it, which means that the answer is $2\,024$.