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?

Combination and permutation are two methods for breaking down a set of objects into smaller groups. Any arrangement is possible when combining the parts of the subset. The parts of the subset are listed in a permutation in some certain order.

Briefing of the given statement:

The "apples and oranges" box needs to be opened, according to the briefing. By definition, the only type of fruit in the box is the one that is inside. Let's imagine you found one apple in the box that was marked with both the words "apples" and "oranges" on the label. You deduce that the box marked "apples" must subsequently only contain apples and that the box marked "oranges" cannot contain only oranges because all of the boxes have supposedly been labeled incorrectly. The box labeled "oranges" must therefore contain both apples and oranges, whereas the box labeled "apples" may only contain 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