If you have a $1 bill a 5 bill a 10 bill and a 20 bill how many different sums of money

You need to find every combinaison of bills.

ex : $1 + 10$   or   5$+10$

I takes for ever to list all the possibilities so you need to think about probabilities to chose a bill.

For each bill, you can add it to your sum or not; so it gives you 2 possibilities; you do that for each bill and you multipliate each what gives you :

2 * 2 * 2 * 2 = 16 different sums