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Mock AMC 8 Problem #3

Mock AMC 8 Problem #3

How many different combinations of $5 bills and$2 bills can be used to make a total of \$17? Order does not matter in this problem.

It says it has 2 ways  but  I found multiple.

Re: Mock AMC 8 Problem #3

There are only 2 ways.

first of all, it says that order does not matter, which means that 5 5 5 2 is the same as 2 5 5 5.

second, there are just 2 ways, once you consider parity. 5 5 5 2 and 5 2 2 2 2 2 2. you cannot have 2 fives, because if you do, once you add the 2s, it will stay even, and 17 is not even.

therefore, there are only 2 solutions