There are 50 five-dollar bills, 20 ten-dollar bills, 15 twenty-dollar bills,
10 fifty-dollar bills, and 5 hundred-dollar bills.  That's

50+20+15+10+5 = 100 bills 

To get $300 with just 3 of those bills, he must draw 3 hundred dollar bills.

There are "5 choose 3"  or 5C3 or 10 ways to draw 3 hundred dollar bills. 

The number of ways he can choose any combination of three bills
from the 100 is "100 choose 3", that is 100C3 = 161700

So the answer is 10/161700 = 1/16170, choice (c).

[Did you know that a study of multiple-choice examinations from schools and
colleges has been done, and it has been determined that choice (c) is by far
more often the correct choice than any other.  So if you ever have to
guess, and can't rule out or give a lower probability to choice (c) being
correct, then always choose (c).    [Hopefully though, you'll never have
to guess!  Wishful thinking, eh?   :-)  ]

Edwin