Answer
$14_{{C}{_{6}}}$ = 3003
Work Step by Step
TOTAL NUMBER OF STANDBY PEOPLE = 14
NUMBER OF SEATS AVAILABLE = 6
THE NUMBER OF WAYS OF SITTING SIX PEOPLE OUT OF FOURTEEN = $14_{{C}{_{6}}}$
= $\frac{14!}{(14 - 6)! 6!}$
= $\frac{14!}{8!. 6!}$
= $\frac{14\times13\times12\times11\times10\times9\times8!}{ 8!.6\times5\times4\times3\times2\times1}$
= $\frac{14\times13\times12\times11\times10\times9}{ 6\times5\times4\times3\times2\times1}$
= 3003