Suppose that you want to buy 9 pieces of fruit from the fruit shop.

The fruits you like are apples, oranges, pears, peaches and grapefruit.

How many different possible combinations can you purchase if you do not necessarily need to buy all of your favourite types of fruit?

For example, some distinct possibilities would be:

9 apples,
7 apples, 2 oranges
2 apples, 7 organges
1 apple, 2 oranges, 6 pears