EXAMPLE 3.2.9

Suppose we are going to use the symbols {a, b, c, d, e, f, g, h} to form a 5-character "password" having no repeated characters. How many different passwords are possible?

SOLUTION

Since forming such a password requires us to choose and arrange 5 letters from this set of 8 letters, the number of different outcomes is

Note: we could have also used the Fundamental Counting Principle to get this answer, since forming a 5-character password requires us to make 5 dependent decisions. The number of outcomoes is

(8) times (7) times (6) times (5) times (5) = 6720