Answer
$3003$ ways
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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To the person on stand-by, it is unimportant whether she is awarded the first, second,..., or sixth seat.
Order is not important, we deal with combinations.
${}_{14}C_{6}=\displaystyle \frac{14!}{(14-6)!6!}=$
$=\dfrac{14\times 13\times 12\times 11\times 10\times 9}{1\times 2\times 3\times 4\times 5\times 6}$
$=3003$
