how many different sums of money can you make using one or more of these bills?

Question

If you have a $1 bill, a $5 bill, $10 bill, and a $20 bill, how many different sums of money can you make using one or more of these bills?

Answer 1

Hello, thank you for taking the time to post your question!

I would break it down based on the number of bills that you use in order to form the sum! The possible unique sums are

Using one bill (4): $1, $5, $10, $20

Using two bills (6): $6, $11, $15, $21, $25, $30

Using three bills (4): $16, $26, $31, $35

Using all four bills (1): $36

So that ends up being 4 + 6 + 4 + 1 = 15 different sums in total

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

The trick to solving this problem is realizing that you need to break it up into parts.  Find the number of totals with one, two, three, or four bills, then add them up.  Since this is a combination problem, you can find each of the numbers with the combination formula, but the numbers are small enough to just think this one out.

 

One Bill: 4 possibilities

Two Bills: 6 possibilities

Three Bills: 4 possibilities

Four Bills: 1 possibility

 

4+6+4+1=15 total different sums of money