We can choose the number of quarters to use 2 ways, 
that is, we can choose to use no quarters, or 1 quarter.
That's 2 ways.

For each of those 2 choices for the number of quarters,
we can choose the number of dimes to use 3 ways, 
that is, we can choose to use no dimes, 1 dime, or 2 dimes.
So we can choose the numbers of quarters and dimes to use
in 2×3 or 6 ways.

For each of those 2×3 or 6 choices for the number of quarters
and dimes to use, we can choose the number of pennies 4 ways, 
that is, we can choose to use no pennies, 1 penny, 2 pennies,
or 3 pennies. So we can choose the numbers of quarters, dimes 
and pennies to use in 2×3×4 or 24 ways. 

No two of those 24 combinations of coins will produce the same 
number of cents, so there are 24 possible numbers of cents 
we can make with 1 quarter, 2 dimes and 3 pennies. 

There are 100 different numbers of cents our bill can have, 

.00, .01, ... .99

So the probability that we can match the "change" part of 
our bill is  or . [ 24% of the time
we can match the "change" and 76% of the time we can't].

Edwin