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

1 Answer
Jul 3, 2016

Assuming that the password is exactly 5 characters in length, and that the characters cannot be repeated, the answers is all the possible permutations of the given letters


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*4 = 20# possible passwords. Now, if the password is 3 letters in length, we have #5*4*3 = 60# possible passwords. Reasoning the same way, if the password is 5 letters in length we have #5*4*3*2*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.