Answer
$17_{{C}{_{8}}}$ = 24310
Work Step by Step
TOTAL NUMBER OF PARENTS OF CHILDREN = 17
NUMBER OF SEATS AVAILABLE IN VAN = 8
THE NUMBER OF WAYS OF SITTING EIGHT PEOPLE OUT OF SEVENTY = $17_{{C}{_{8}}}$
= $\frac{17!}{(17 - 8)! 8!}$
= $\frac{17!}{9!. 8!}$
= $\frac{17\times16\times15\times14\times13\times12\times11\times10\times9!}{ 9!.8\times7\times6\times5\times4\times3\times2\times1}$
= $\frac{17\times16\times15\times14\times13\times12\times11\times10}{ 8\times7\times6\times5\times4\times3\times2\times1}$
= 24310
