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A person writes letters to 5 friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least 2 letters are in the wrong envelopes?
- (A) 119
- (B) 120
- (C) 121
- (D) 122
Correct answer: (A) 119
Solution
Total ways = 5! = 120. Arrangements with 0 wrong (all correct) = 1. Arrangements with exactly 1 wrong = 0 (impossible: if exactly 1 letter is wrong, another must also be wrong). At least 2 wrong = 120 - 1 - 0 = 119.
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