A person has 5 coins of different values. ¿How many different additions can I make?

Question

ranga · Answer

Is the question how many different additions can you make or how many different changes can you make with 5 coins?

osanseviero · Answer

Sums

osanseviero · Answer

I saw 31 as a result in some website, but I would like someone to explain how to solve this

ranga · Answer

To do additions you have to have at least 2 coins. 
You can select 2 coins in 5C2 ways.
With three coin additions: 5C3 ways 
With four coin additions: 5C4 ways 
With five coin additions: 5C5 ways 
Add them all up.

ranga · Answer

But if you count the single coins itself (no additions) then 5C1 ways.  So you add them all and you get 31.  So when they say "sums" they don't mean additions but how many different changes can you make with 5 coins.

osanseviero · Answer

Oh...so it is 26, but if you can use the coins by themselves, you add 5. Thanks :D

ranga · Answer

yes. you are welcome.