# How many ways can the letters P Q C N Z be arranged to make a password?

We have 5 different possibilities for the first letter in the password, and once we have selected the first, since we cannot repeat any letter, we have 4 possibilities for the second. So, if the password has only 2 letters, we have $5 \cdot 4 = 20$ possible passwords. Now, if the password is 3 letters in length, we have $5 \cdot 4 \cdot 3 = 60$ possible passwords. Reasoning the same way, if the password is 5 letters in length we have $5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 = 120$ possible passwords. This is the total number of permutations of the 5 letters, called 5 factorial, and expressed as 5! in mathematical notation.