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* .

*how many ways to make*change for one

*dollar*using nickels, dimes and. Actually there are over 293 ways to use

*coins*to

*make a dollar*!

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 .