How do I solve this?

Question

A computer password can use all digits (0-9) and all letters (a-z) that are case sensitive (upper and lower). How many different permutations of 5-figure passwords are there if there is no repeated input? 

Answer 1

This is a simple permutations problem! Let's understand, analyze and solve !

 

First, we understand that there are five spaces that need to be filled: _ _ _ _ _

 

Second, we should know HOW MANY can go in those spaces: as the problem says, ANY number 0-9,or capital letters,or lower case letters. Numbers 0-9 give us 10 options, all lowercase letters give 26 options, and capital letters give us 26 options. Adding these together, that is 62 options.

 

Third, we see that since each space can give 62 options (as numbers and letters can be repeated), you multiply 62 by itself five times: 62 * 62 *62 *62 *62. This gives us 916132832 permutations for a password!

 

**For future reference, it is good to note that if the problem said "each letter, lowercase letter, or capital letter can only be used once". then the answer would be 62 * 61 * 60 * 59 * 58. The reason for this is that once a letter or number is used, it must be removed from the "options" total that we figured out in the 2nd paragraph above. So at first you have all 62 options, but once one is picked it cant be used in the second slot, so now there are only 61 options, so on and so forth.