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Mock AMC 8 Problem #3

 
 
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Mock AMC 8 Problem #3
by Eric Lu - Wednesday, October 30, 2019, 5:09 PM
 

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.

 
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Re: Mock AMC 8 Problem #3
by Jeffrey W. - Saturday, November 30, 2019, 9:01 AM
 
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