Answer
The ways to select different groups of 8 children out of 17 children to drive them to the zoo are $24,310$.
Work Step by Step
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:
$\begin{align}
& ^{17}{{C}_{8}}=\frac{17!}{8!\left( 17-8 \right)!} \\
& =\frac{17!}{8!9!} \\
& =\frac{17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9!}{\left( 9! \right)\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1} \\
& =24,310
\end{align}$
