Question

Suppose a person may use any six different letters except a, e, i, o, or u, to make a computer password. Using permutations, find the number of possible six-letter, lower-case passwords.

Answer 1

39,070,080 possible passwords

Explanation:

The complete alphabet has 26 letters. Removing the 5 vowels, we have 21 letters.

We want to make groups of 6 letters, and the order of each letter matters, because it will create a different password, so we can write a permutation to solve this problem.

The number of elements is 21, and the group has 6 elements, so we have a permutation of 21 choose 6:

P(21,6) = 21! / (21-6)! = 21! / 15! = 21 * 20 * 19 * 18 * 17 * 16 = 39,070,080 possible passwords