Password Permutations

Question

Could somebody answer me how many possibilities are there for a six-letter (only letters, but case-sensitive) computer password? Is it $^{52}C_6 \times 6!$ ?

Answer 1

Using a combination means you cannot select the same letter twice, so this will not give you the right answer.

Instead, build the password letter by letter and ask yourself how many choices you have at each step. For the character of the password, you can pick any of the $52$ options. For the second character, you can still pick any of the $52$ letters, since we are allowing repeats. Continuing in this way, you can form the password in $$ 52 \cdot 52 \cdot 52 \cdot 52 \cdot 52 \cdot 52 = 52^6 \text{ ways}. $$