How many ways to fill the bag with fruits?

Probability Level 3

You have to fill a large bag with 2018 fruits—apples, bananas, cantaloupes, durians, and raspberries—under the following restrictions:

  • The number of apples must be a multiple of 41.
  • The number of bananas must be even.
  • There cannot be more than 40 cantaloupes.
  • There cannot be more than one durian (for obvious reasons).

How many different ways are there to fill the bag?

Note: This problem can be solved without having to grind all the possibilities. Generating functions may help you.


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