A person writes letters to six friends and their addresses to corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in wrong envelopes?

  • 6
    $\begingroup$ Note: you can never have only $1$ letter in the wrong envelope. $\endgroup$ Sep 7, 2018 at 10:20
  • 2
    $\begingroup$ @MohammadZuhairKhan - you can if one envelope is empty and another contains two letters, though this question probably assumes each envelope contains exactly one letter $\endgroup$
    – Henry
    Sep 7, 2018 at 10:53

1 Answer 1


If the person is placing the letters in the envelopes at random, and the order matters, there will be $6! = 720$ ways of placing the letters, and only of those has all of the letters placed correctly. So there are $719$ ways of making a mistake. (Note that one mistake means at least 2 are incorrect)


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