Question

There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, how can you immediately label all of the boxes correctly?.

1. The correct option is C
Containing both apples and oranges.

### What exactly are permutations and combinations?

Two techniques for dividing a set of objects into smaller groups are combination and permutation. Combining the components of the subset allows for any configuration. A permutation with the components of the subset listed in a specific order.

### Brief explanation of the stated fact:

The briefing states that the “apples and oranges” box needs to be opened. The fruit that is within the box is the only type of fruit there is, so to speak. Imagine you discovered one apple in the container that was labeled with the words “apples” and “oranges” as well. You conclude that since all the boxes have allegedly been improperly labeled, the box labelled “apples” must logically contain only apples, and the box marked “oranges” cannot contain only oranges. In contrast to the box marked “apples,” which may only include apples, the box marked “oranges” must contain both apples and oranges.
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I understand that the question you are looking for is:
There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, you can immediately label all of the boxes correctly. Which box did you open?
A. Containing apple
B. Containing oranges
C. Containing both apples and oranges
D. Cannot be determined