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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.

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Answer #1

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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