A computer system uses passwords that contain exactly 4 characters, and each character is 1 of the 26 lowercase letters (a-z) or 26 uppercase letters (A-Z) or 10 integers (0-9). 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 that contain at least 1 integer. Report the exact number.

Question

Mathematics

Skyla

22 October, 08:00

A computer system uses passwords that contain exactly 4 characters, and each character is 1 of the 26 lowercase letters (a-z) or 26 uppercase letters (A-Z) or 10 integers (0-9). 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 that contain at least 1 integer. Report the exact number.

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Alana Dickson · Answer 1

The number of passwords that contain at least one integer is 9,533,120.

Step-by-step explanation:

If you have a 4 char password, we can calculate the number of passwords that start with an integer:

We have 10 integers to choose, and then 10+26+26 = 62 possibilities for each of the remaining characters.

So we have:

10*62*62*62 = 2,383,280 possibilities

Because we can have integers in anyone of the four characters, we can multiply this number by 4

2,383,280 * 4 = 9,533,120 possibilities