In how many ways can you change a $20 bill using $10 bills, $5 bills, $2 bills, and $1 bills?
$1 $2$5$10
1 = 20 0 0 0
2 = 18 1 0 0
3 = 16 2 0 0
4 = 14 3 0 0
5 = 12 4 0 0
6 = 10 5 0 0
7 = 8 6 0 0
8 = 6 7 0 0
9 = 4 8 0 0
10 = 2 9 0 0
11 = 0 10 0 0
12 = 15 0 1 0
13 = 13 1 1 0
14 = 11 2 1 0
15 = 9 3 1 0
16 = 7 4 1 0
17 = 5 5 1 0
18 = 3 6 1 0
19 = 1 7 1 0
20 = 10 0 2 0
21 = 8 1 2 0
22 = 6 2 2 0
23 = 4 3 2 0
24 = 2 4 2 0
25 = 0 5 2 0
26 = 5 0 3 0
27 = 3 1 3 0
28 = 1 2 3 0
29 = 0 0 4 0
30 = 10 0 0 1
31 = 8 1 0 1
32 = 6 2 0 1
33 = 4 3 0 1
34 = 2 4 0 1
35 = 0 5 0 1
36 = 5 0 1 1
37 = 3 1 1 1
38 = 1 2 1 1
39 = 0 0 2 1
40 = 0 0 0 2
