In how many ways can you change a 20 dollar bill using 10 dollar bills, 5 dollar bills, 2 dollar bills, and 1 dollar bills?
There are 40 ways of making a change for a $20 bill as follows:
$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)
