Neco 2023 Data Processing Question 38

A company enforces a password policy: passwords must be exactly \(8\) characters long and contain at least one uppercase letter (\(26\) choices), one lowercase letter (\(26\) choices), one digit (\(10\) choices) and one special character (\(10\) choices). Characters may repeat. An attacker knows the policy and tries random passwords that satisfy it, each attempt independent.\n\n(a) Using inclusion‑exclusion, determine the total number of possible passwords that satisfy the policy.\n\n(b) Assuming the attacker makes \(10\) independent attempts, calculate the probability that the correct password is guessed within those \(10\) attempts.\n\n(c) The security guideline requires this probability to be less than \(10^{-6}\). Does the policy meet the guideline?