$20 + $20 + $10

$20 + $20 + $5 + $5

.

.

.

$20 + $10 + $5 + $5 + $10

.

.

.

$10 + $5 + $5 + $20 + $10

.

.

.

$5 +$5 + $5 + $5 + $10 + $10 + $5 + $ 5

.

.

.

$5 + $5 + $5 + $5 + $5 + $5 + $ 5 + $5 + $5 + $5

The pattern : 4 x 4 x 2 x 1 = 32 ways.

There are 4 ways to make up a $20 -- ($20), ($10 $10), ($10 $5 $5) and ($5 $5 $ 5$ 5)

There are 2 ways to make up a $10 -- ($10) and ($5 $5)

There is 1 way to make up a $5 -- ($5)

So the total ways is the product of these ways -- or 32 ways, since the top way is $20 $20 $10 (the fewest bills, which can all be broken down), and the bottom way is all $5 bills (the most bills, which can not be broken down any smaller).

$20 + $20 + $5 + $5

.

.

.

$20 + $10 + $5 + $5 + $10

.

.

.

$10 + $5 + $5 + $20 + $10

.

.

.

$5 +$5 + $5 + $5 + $10 + $10 + $5 + $ 5

.

.

.

$5 + $5 + $5 + $5 + $5 + $5 + $ 5 + $5 + $5 + $5

The pattern : 4 x 4 x 2 x 1 = 32 ways.

There are 4 ways to make up a $20 -- ($20), ($10 $10), ($10 $5 $5) and ($5 $5 $ 5$ 5)

There are 2 ways to make up a $10 -- ($10) and ($5 $5)

There is 1 way to make up a $5 -- ($5)

So the total ways is the product of these ways -- or 32 ways, since the top way is $20 $20 $10 (the fewest bills, which can all be broken down), and the bottom way is all $5 bills (the most bills, which can not be broken down any smaller).