Precalculus (6th Edition) Blitzer

The number of ways to select 8 books out of 40 books is $76,904,685$.
We know that: ${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$ So, from the information, \begin{align} & n=40 \\ & r=8 \end{align} Then, we know that to find the number of combinations of 40 things taken 8 at a time, we applying the above formula: \begin{align} & {}_{40}{{C}_{8}}=\frac{40!}{8!\left( 40-8 \right)!} \\ & =\frac{40!}{8!32!} \\ & =\frac{40\times 39\times 38\times 37\times 36\times 35\times 34\times 33\times 32!}{8!\times 32!} \\ & =76,904,685 \end{align} Thus, the number of ways to select 8 books out of 40 books are $76,904,685$.