with the assumption that the coins are identical and the choose order does not matter:
only two of the coin numbers are independent, the third (# quarters) is given by Q=20-N-D
then
nickels=0_____dimes=20 options (the 20 options of quarters are not independent so we don't look at that)
nickels=1_____dimes=19 options
nickels=2_____dimes=18 options
.
.
.
nickels=20____dimes=0 options
then the solution is the sum (using sigma notaiton)
20
E i
i=0
which is 210