number of strings of $5$ lower case letters $a\cdots z$ that do not contain any letter twice or more What are the number of strings of $5$ lower case letters $a\cdots z$  that do not contain any letter twice or more?
I think it would be $26*25*24*23*22$  because the first position can be filled in $26$ ways because there are $26$ possible lowercase characters; the second one in $25$ ways and so on 

community wiki answer so the question can be closed
Your answer is correct.
