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A computer system uses passwords that contain exactly 5 characters, and each character is 1 of...

A computer system uses passwords that contain exactly 5 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 A′∩ B′. Report the exact number.

Math   Statistics-And-Probability   
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Answer #1

A contain all the passwords with only letters, therefore A' contain all the passwords which either have all the numbers or have at least one number and one alphabet.

Similarly, B is set of all passwords with only integers, therefore B' contain all the passwords with either all alphabets or with at least one alphabet and one number.

Therefore the set r A′∩ B′ would contain all the passwords with at least one number and at least one alphabet.

The number of passwords in r A′∩ B′ is computed here as:

= Total number of possible passwords - Number of passwords with only numbers - Number of passwords with only alphabets.

Note that there are a total of 11 characters and each can be used in each of the 5 locations. Similarly with 6 alphabets, number of passwords with only alphabet is given as 65 and so on..

therefore 150150 passwords are there in the given set.

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