$3.$ My friend is working on password$-$cracking, so he wants to try and test all possible passwords to check system security. He says that he has a developed a secret algorithm. If you give his algorithm a set of n letters from the English alphabet, it will print them in every possible order. My friend says the algorithm runs in O$($n$2).$ Is this possible? If it is not possible, what is the fastest possible algorithm that can solve this problem? Justify your answer with a precise argument. $[4$ marks$]$