Salma is choosing a -letter password from the letters A, B, C, D, and E. The password cannot have the same letter repeated in it. How many such passwords are possible?

Question

Salma is choosing a 3

-letter password from the letters A, B, C, D, and E. The password cannot have the same letter repeated in it. How many such passwords are possible?

Answer 1

A factorial is an positive integer, multiplied by all the positive integers below it. For example, 5 factorial is 5 * 4 * 3 * 2 * 1.

Salma has five possible letters to choose from for the first letter of the password. So she has 5 options. A letter is now used up, so she has only four options for the second letter, and three options for the third letter.

The answer is 5 * 4 * 3 = 60 possible combinations. This is a similar idea to 5 factorial, except we multiply from 5 downward only until reaching 3 and then stop (we don't multiply by 2).