How many ways can you add the numbers 1-5, USING ONLY 5 NUMBERS, to get a total of 15 or less. You may use numbers more than once

Question

1,1,1,1,1 is a possibility since it is less than 15. list the possible outcomes

 

1,2,1,1,1 is a different outcome than 1,1,2,1,1. 

 

ORDER DOES MATTER

Answer 1

Hi Mark,

 

I think what you're looking for is related to something called "compositions". Try the the Wikipedia page on Composition (combinatorics). A related concept is called "partition", which is more common but with partitions order doesn't matter.

 

You'll have to do more work for 7, ..., 15 since some compositions for these numbers are formed using numbers greater 5.