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There are 4 letters and 4 addressed envelopes. If each letter is randomly placed in an envelope, the number of ways in which only one letter goes in the wrong envelope isChoices:- 43 4C1+4C2+4C3+4C44C1+4C2+4C3+4C4 4C0+4C1+4C2+4C34C0+4C1+4C2+4C3 0

Question

There are 4 letters and 4 addressed envelopes. If each letter is randomly placed in an envelope, the number of ways in which only one letter goes in the wrong envelope isChoices:- 43 4C1+4C2+4C3+4C44C1+4C2+4C3+4C4 4C0+4C1+4C2+4C34C0+4C1+4C2+4C3 0

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Solution

The question is asking for the number of ways in which only one letter goes in the wrong envelope. This is a problem of derangements, also known as the "hat-check problem".

In this case, we have 4 letters and 4 envelopes, and we want to find the number of ways to place the letters in the envelopes such that only one letter is in the correct envelope.

This is a tricky problem because when one letter is in the correct envelope, it forces at least one other letter to also be in the correct envelope. This is because the remaining letters cannot all be in the wrong envelopes (which would be a derangement), as that would contradict our assumption that only one letter is in the correct envelope.

Therefore, the answer to this problem is 0. There are no ways to place the letters in the envelopes such that only one letter is in the correct envelope.

This problem has been solved

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