Acomputer 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.

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