Answer
$ 210$
Work Step by Step
First we ask, does order of selection matter?
Being selected first or fourth does not matter, you are a commissioner either way.
Order does not matter, we use combinations.
Combinations Formula:
The number of combinations possible if $r$ items are taken from $n$ items is
${}_{n}C_{r}=\displaystyle \frac{n!}{(n-r)!r!}$
r=4 candidates are taken from n=10 candidates.
${}_{10}C_{4}=\displaystyle \frac{10!}{(10-4)!4!}=\frac{10\times 9\times 8\times 7\times 6!}{6!\cdot 4!}$
... reduce the fraction by 6!
$ =\displaystyle \frac{10\times(9\times 8)\times 7 }{(4\times 3\times 2)\times 1}\qquad$... reduce the fraction
$=10\times(3)\times 7 $
$=210$
