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In each combination, you can have 0,1,2 or 3 pennies; you can also have 0 or 1 nickels, 0 or 1 dimes and 0 or 1 quarters. That is, 4 ways of picking the number of pennies, 2 ways of picking how many nickels, 2 for dimes and 2 for quarters. In all that makes 4*2*2*2 = 32 combinations.

BUT, one of these combinations is where you have 0 pennies, 0 nickels, 0 diems and 0 quarters. Conventionally, a null combination such as this is omitted and so you have 31 valid combinations.

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Q: If you have 3 pennys 1 nickel 1 dime 1 quarter how many different combinations can you make?

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