Question

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.

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