How many different ways can you make change for a quarter? (Different arrangements of the same coins are not counted separately.)

How many different ways can you make change for a quarter?
(Different arrangements of the same coins are not counted separately.)
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Liyana Mansell
There are three coins that are less than a quarter (0.25$) in value,that is a penny (0.01$), a nickel (0.05$) and a dime (0.10$).
Possibilities are then:
2 dimes 1 nickel
2 dimes and 5 pennies
1 dime and 3 nickels
1 dime and 2 nickels and 5 pennies
1 dime and 1 nickel and 10 pennies
1 dime and 15 pennies
5 nickels
4 nickels and 5 pennies
3 nickels and 10 pennies
2 nickels and 15 pennies
1 nickel and 20 pennies
25 pennies
THUS there are 12 possibilities
Result: 12