Let be the number of ways to prepare a fruit basket with r pieces of fruit. We want to find the Ordinary Power Series Generating Function (OPSGF) .
The OPSGF for the number of apples is
the series for the number of bananas is the same,
and the series for the number of oranges is
The number of ways to get 36 pieces of fruit in the basket is the coefficient of when f is expanded as a series.
Do you see how to find this coefficient?