Different Coins
How many different ways can you make change for a dollar using 5, 10, 20 and 50c coins?
How many different ways can you make change for a dollar using 5, 10, 20 and 50c coins?
Please EXPLAIN and show STEP BY STEP METHODOLOGY.
Please include written explanations detailing the processes used to solve the problem.
Thanks 
, looking for the best answer!
Since you’ll always have a multiple of 5 when mixing these coins, you can always use 5c pieces to make up the rest if you have a combination of the others that makes less than $1. So the question is equivalent to asking how many ways can 10, 20 and 50c coins be used to make <= 100c.
Now, you can always arrange each assortment of coins so the 50c coins are first, then 20c, then 10c. So we'll start with the possibilities for numbers of 50c coins, then for each of those the possibilities for numbers of 20c coins, etc.
0x 50c:
For this we can have zero 20c pieces, or 1, or 2, 3, 4, or 5 20c pieces (5 possibilities), and for each of these we can add 10c pieces as well for an additional 10, 8, 6, 4, 2, 0 possibilities respectively. This makes the total possibilities for the 0x 50c branch: 5 + 10 + 8 + 6 + 4 + 2 + 0 = 35
1x 50c:
For this we can have zero 20c pieces or 1 or 2 20c pieces (3 possibilities), and for each of these we can add 10c pieces as well for an additional 5, 3, 1 possibilities respectively. This makes the total possibilities for the 1x 50c branch: 3 + 5 + 3 + 1 = 12
2x 50c:
Only 1 possibility as this makes $1.
In total, 35 + 12 + 1 = 48.
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