How many ways can you make change for a $50 bill using $5, $10, and $20 bills?

There are 12 ways to make change for a $50 bill using $5, $10 and $20 bills

Step-by-step explanation:

Let's write down every possibility starting by using the largest quantity of $20 bills and we'll go from there, everytime that we get a $10 bill we will split it in the next option into 2 $5 bills.

(20) (20) (10)

(20) (20) (5) (5)

(20) (10) (10) (10)

(20) (10) (10) (5) (5)

(20) (10) (5) (5) (5) (5)

(20) (5) (5) (5) (5) (5) (5)

Now we start with the largest quantity of $10 bills (5) and go from there, splitting them into two 5 dollar bills in the next option.

(10) (10) (10) (10) (10)

(10) (10) (10) (10) (5) (5)

(10) (10) (10) (5) (5) (5) (5)

(10) (10) (5) (5) (5) (5) (5) (5)

(10) (5) (5) (5) (5) (5) (5) (5) (5)

(5) (5) (5) (5) (5) (5) (5) (5) (5) (5)