Artificial intelligent assistant

4 different letters and 4 addressed envelopes. Question is : In how many ways can the letters be put into the envelopes, so that at least one letter goes to the correct address ? Answer is 15. All i could think of is : 4 envelop choices for each letter, so 4*4 = 16. A little fertilizer for my withered grey-matter ?

$$4!-!4=24-9=15$$

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