I have five apples and ten oranges. If a fruit basket must contain at least one piece of fruit, how many kinds of fruit baskets can I make?  (The apples are identical and the oranges are identical.  A fruit basket consists of some number of pieces of fruit, and it doesn't matter how the fruit are arranged in the basket.)
This is a problem about counting combinations, where the order of the fruit does not matter. One way to approach this is to consider how many apples I can choose for the basket, and then how many oranges I can choose for the basket, and then multiply those numbers to get the total number of baskets. For the apples, I can choose anywhere from zero to five, inclusive. That gives me six possible choices. For the oranges, I can choose anywhere from zero to ten, inclusive. That gives me eleven possible choices. However, there is one case where I would not have a valid basket, and that is if I choose zero apples and zero oranges. So I need to subtract one from the total number of baskets. Therefore, the total number of baskets I can make is 6 times 11 minus 1, which is 65. 