Question 981579: a vending machine accepts nickel, dimes and quarters. exact change is needed to make a purchase. How many ways can a person with five nickels, three dimes and two quarters make a 75-cent purchase from the machine
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
The sum of the values of the nickels and the dimes is 55 cents. Therefore you need to use at least one quarter. So...
If you use 1 quarter, you have to make up the additional 50 cents out of the 55 cents worth of dimes and nickels. Obviously there is only one way to do this unless you had some way of differentiating between the nickels. For example, if you painted a dot of nail polish on each of the nickels each in a different color, then there would be 5 ways to exclude one nickel from the set, however I suspect that this is not something your instructor intended. I only include this discussion as a lesson to both you and your instructor about the importance of precision in language; particularly when you are dealing with mathematics.
The only other alternative is to use two quarters. Then you must make up the remaining 25 cents from three dimes and five nickels. Three dimes doesn't work, so there are only three possibilities for the number of dimes, namely zero, one, and two dimes. I'll let you finish this analysis for yourself.
John
My calculator said it, I believe it, that settles it
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