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?.

Answer 1

The correct option is C

Containing both apples and oranges

What is permutation and combination?

A set of items can be divided into subsets in two different ways: combination and permutation. The components of the subset may be arranged in any order when combined. The subset's components are listed in a permutation in a certain order.

Briefing:

The box with the words "apples and oranges" must be opened. By definition, the fruit in the box is the sole type of fruit it contains. Let's say you discovered an apple in the box that had both apples and oranges listed on the label. Since you know it must consequently only contain apples, you draw the conclusion that the box labeled "oranges" cannot contain only oranges because all boxes have allegedly been mislabeled. As a result, the box marked "oranges" must have both apples and oranges while the box marked "apples" can only include 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