There are 4 different letters and 4 addressed envelops. In how many ways can…
2026
There are 4 different letters and 4 addressed envelops. In how many ways can the letters be put in the envelops so that at least one letter goes to the correct address?
Answer: C. 15 — Answer: 15 Total ways to place 4 letters into 4 envelopes: 4! = 24. Number of ways when no letter is in its correct envelope (derangements D4): Use the…
- A.
11
- B.
12
- C.
15
- D.
16
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Show answer & explanation
Correct answer: C
Answer: 15
Total ways to place 4 letters into 4 envelopes: 4! = 24.
Number of ways when no letter is in its correct envelope (derangements D4):
Use the derangement formula Dn = n! * sum_{k=0}^n (-1)^k / k!. For n = 4:
D4 = 4! * (1 - 1/1! + 1/2! - 1/3! + 1/4!) = 24 * (1 - 1 + 1/2 - 1/6 + 1/24) = 24 * 0.375 = 9.
So the number of arrangements with at least one letter correctly placed = 24 − 9 = 15.