Puzzle #204: $17.35

How many ways can you express $17.35 in Canadian bills and change?

There is one additional proviso: any combination may not have more than two of any denomination.

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, May 3, 2017 at noon Pacific Time. I will post the answer shortly after.