how many ways can you make 45 cents with pennies ,dimes, nickels, and quarters?
If you need all 4 kinds of coins, then you must have a multiple of 5 pennies.
5p+n+d+q = 45
Since you only have one of each of the larger coins, there's no other way to include all 4 kinds.
If some kinds may be omitted, then just start working your way through the various combinations. Not hard, but you need to watch the details.