Four letters are placed at random into four addressed envelopes, one letter per envelope. What is the probability that at least one letter goes into its correct envelope?
Answer and explanation
Correct answer: D.
- Step 1: The total number of ways to distribute letters into envelopes is .
- Step 2: Calculate the number of derangements (where no letter is in the correct envelope): .
- Step 3: The number of distributions with at least one correct letter is . Thus, the probability is .
Answer
.
Why not the others: is the probability of complete derangement (); assumes equal chance of derangement; computes probability for 3 envelopes; is an arithmetic estimation error.
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