Answer
$24,310$ groups
Work Step by Step
A combination from a group of items occurs when no item is used more than once and the order of items makes no difference.
The number of combinations possible if $r$ items are taken from $n$ items is
${}_{n}C_{r}=\displaystyle \frac{n!}{(n-r)!r!}$
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When selecting children to drive, it is unimportant which is selected first, second,..., or eighth.
Order is not important, we deal with combinations.
${}_{17}C_{8}=\displaystyle \frac{17!}{(17-8)!8!}$
$=\displaystyle \frac{17\times 16\times 15\times 14\times 13\times 12\times 11\times 10}{1\times 2\times 3\times 4\times 5\times 6\times 7\times 8}$
$=\displaystyle \frac{17\times 1\times 1\times 1\times 13\times 1\times 11\times 10}{1\times 1\times 1\times 1\times 1\times 1\times 1\times 1}$
$=24,310$
