We can't have an odd number of quarters, because an odd number
of 25s would make up a number of cents that would end with a 5,
and since we have no nickels, it would be impossible to make
$3.00 using an odd number of quarters. So we can only have an
even number of quarters.
If we don't use any 1-dollar bills, we can have 0,2,4,6,8,10,or 12
quarters and the rest, if any, all in dimes.
That's 7 ways.
If we use one 1-dollar bill, we can have 0,2,4,6, or 8 quarters, and
the rest, if any, all in dimes.
That's 5 more ways.
If we use two 1-dollar bill, we can have 0,2, or 4 quarters, and
the rest, if any, in dimes.
That's 3 more ways.
Then there's one more way, 3 1-dollar bills.
So that's 7 + 5 + 3 + 1 = 16 ways to have $3 using only 1-dollar bills,
quarters and dimes.
Edwin
