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jmc

counting and probability senior

Problem

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.)
Solution
For a moment, consider empty fruit baskets. Now there are choices total for the apples: no apples, one apple, two apples, three, four, or all five apples. Similarly, there are choices total for the oranges. Thus, there are potential fruit baskets. But we must subtract one off of that because we counted empty fruit baskets, which aren't actually allowed. So there are possible fruit baskets.
Final answer
65