Question

In how many 5 letters can go to 5 envelopes such that exactly one is in its correct

Answer 1

hello

5 letters can go into 5 envelopes in 5! ways, i.e. 5! = 120, and there is just 1 combination in which each and every letter goes to its corresponding envelope, thus 120-1=119 for first condition  

1 letter in its correct corresponding envelope and 4 others juggled, here we get 4! = 24 again we should subtract 1 combination in which all 4 letters can go correctly to their respective envelopes, thus 24-1 = 23 for Second condition.  

To sum up, 119+23 = 142 ways.  

Please, correct if I went away