How many combinations of pennies, dimes, nickels, and quarters create 0.32$? I need help solving this. I cannot find the complete number of combinations. I have already found $5$, but I can't find any more.

First consider quarters.  You could have either no quarters (leaving $32$ cents to be covered by pennies, nickels and dimes) or one quarter (leaving $7$ cents).  Diagram:
     (32) 
  [0 quarters]        [1 quarter]         
     (32)                (7)

Next, consider dimes.  In the first case you could have 0, 1 or 2 dimes, in the second you must have 0.  Diagram:
     (32)
  [0 quarters]                              [1 quarter]         
     (32)                                      (7) 
[0 dimes]    [1 dime]    [2 dimes]          [0 dimes]
  (32)         (22)         (2)                (7)

Next consider nickels.  Finally, everything left over must be done with pennies.
