Breaking a dollar
Probability
Level
pending
Find the number of ways of breaking a dollar bill into change, coins come in the denominations .
The answer is 292.
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1 solution
Given that one 50-cent coin will be used, there are 50 combinations:
another 50c (1 way).
2 25c (1 way).
1 25c with: 2 10c (2 ways), 1 10c (4 ways), or 0 10c (6 ways).
no 25c with: 5 10c (1 way), 4 10c (3 ways), 3 10c (5 ways), 2 10c (7 ways), 1 10c (9 ways), or no 10c (11 ways).
Given that no 50-cent coins will be used, there are 242 combinations:
4 25c (1 way).
3 25c with: 2 10c (2 ways), 1 10c (4 ways), or no 10c (6 ways).
2 25c with: 5 10c (1 way), 4 10c (3 ways), 3 10c (5 ways), 2 10c (7 ways), 1 10c (9 ways), or no 10c (11 ways).
1 25c with: 7 10c (2 ways), 6 10c (4 ways), 5 10c (6 ways), 4 10c (8 ways), 3 10c (10 ways), 2 10c (12 ways), 1 10c (14 ways), or no 10c (16 ways).
no 25c with: 10 10c (1 way), 9 10c (3 ways), 8 10c (5 ways), 7 10c (7 ways), 6 10c (9 ways), 5 10c (11 ways), 4 10c (13 ways), 3 10c (15 ways), 2 10c (17 ways), 1 10c (19 ways), or no 10c (21 ways).
Total: 292 ways.