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# A computer system uses passwords that contain exactly 4 characters, and each character is 1 of...

A computer system uses passwords that contain exactly 4 characters, and each character is 1 of the 3 lowercase letters (a, b, c) or 3 upper case letters (A, B, C) or the 5 odd digits (1, 3, 5, 7, 9). Let Ω denote the set of all possible passwords, and let A and B denote the events that consist of passwords with only letters or only integers, respectively. Determine the number of passwords for Ω. Report the exact number.

Given no. of characters in each password in set Ω is 4

There are 3 + 3 + 5 = 11 choices for each letter of the password (each character can be one of the 3 lowercase letters or one of the set 3 upper case letters or one of the 5 odd digits).

Hence, no. of passwords for Ω

= No. of ways in which each password can be chosen

= 11 * 11 * 11 * 11 = 14641

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