## Precalculus (6th Edition) Blitzer

The ways to select different groups of 8 children out of 17 children to drive them to the zoo are $24,310$.
We know that: $^{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$ So, from the information, \begin{align} & n=17 \\ & r=8 \end{align} Then, we have to find the number of combinations of 17 things taken 8 at a time: \begin{align} & ^{17}{{C}_{8}}=\frac{17!}{8!\left( 17-8 \right)!} \\ & =\frac{17!}{8!9!} \\ & =\frac{17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9!}{\left( 9! \right)\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1} \\ & =24,310 \end{align}