Question

Twenty-five crates of apples are delivered to a store. The apples are of three different sorts, and all the apples in each crate are of the same sort. Show that among these crates there are at least nine containing the same sort of apple.

a) True
b) False

Answer 1

Among the twenty-five crates, there are at least nine containing the same sort of apple.

Step-by-step explanation:

To show that among the twenty-five crates there are at least nine containing the same sort of apple, we can use the Pigeonhole Principle.

Since there are three different sorts of apples and only 8 crates of each sort would be needed to have 24 different crates, if we have 25 crates, at least 9 of them must contain the same sort of apple.