Case (1): It is impossible to have 19 coins of the same type that equal one dollar. Case (2): There are TWO ways to have one dollar using only two types of coins.
However, if the question were how many ways there are to make change for a billion (in the sense of thousand million) dollars, using only the same coins .
The question was simple enough: How many different ways are there to make change. . be split into two coins (i.e, dime, half-dollar), you can make the next one .