Question

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

Answer 1

12 ways

Explanation:

20 x 20 x 10 x 20 x 20 x 5 x 5

Answer 2

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

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)