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.

Accepted Solution

Answer: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 42,383,280 * 4 = 9,533,120 possibilities