There are 3 types of apples in a basket: 7 Red Delicious apples, 8 Gala apples, and 9 Granny Smith apples. Without looking, what is the fewest number of apples you need to take out of the basked to guarantee that you have at least 2 different types of apples?
10
To determine the fewest number of apples you need to take out of the basket to guarantee that you have at least 2 different types of apples, you can consider the worst-case scenario.
The worst-case scenario is when you initially pick all the apples of one type. In this case, let's assume you pick all the 7 Red Delicious apples. Now, you need to pick apples of a different type, either Gala or Granny Smith apples.
Since there are 8 Gala apples and 9 Granny Smith apples remaining, you will need to pick 8 more apples to guarantee that you have at least 2 different types of apples. This is because even if you pick all 8 Gala apples, you may end up with all Gala apples and no Granny Smith apples. Therefore, you need to pick an additional apple to ensure that you have at least one Granny Smith apple.
So, you will need to pick a total of 7 (Red Delicious) + 8 (Gala) + 1 (Granny Smith) = 16 apples to guarantee that you have at least 2 different types of apples.