We need to determine the combination of the 76 books taken 3 by 3. To do this, we have to use the following expression:
[tex]C_{n,p}=\frac{n!}{p!(n-p)!}[/tex]Where n is the number of elements in the group, p is the number of elements in the subgroup and C is the number of total combinations. So we have:
[tex]\begin{gathered} C_{76,3}=\frac{76!}{3!(76-3)!} \\ C_{76,3}=\frac{76!}{3!(73)!} \\ C_{76,3}=\frac{76\cdot75\cdot74\cdot73!}{3!\cdot73!} \\ C_{76,3}=\frac{76\cdot75\cdot74}{3\cdot2\cdot1} \\ C_{76,3}=\frac{421800}{6}=70300 \end{gathered}[/tex]Thre are 70300 ways he can select the books.
