How many different passwords can be created using 6 numbers or letters with no repetition?

Question

A password is required to log into a system that only recognizes numbers and letters of the alphabet (not case sensitive). You want to create a password using 6 numbers or letters, but cannot reuse any of them.

How many different passwords are possible?

Answer 1

With 26 letters and 10 numerical digits available, we have 36 choices for the first spot. Since we cannot reuse whatever we use, this leaves 35 options for the second, 34 for the third, 33 for the fourth, 32 for the fifth, and 31 for the sixth. The total number of possibilities would then be 36 x 35 x 34 x 33 x 32 x 31, which is equal to 1402410240 possible passwords.