2014 MI P2 Q11

A machine is used to generate codes consisting of \(4\) characters. A character is either one of the \(26\) letters of the alphabet A – Z or one of the \(10\) digits \(0-9\). Each of the \(36\) characters are equally likely to be generated and each character can be generated more than once.

Find the probability that a randomly generated code has

1. no digits,[1]
2. the first two characters consisting of digits and the first digit is higher than the second digit,[2]
3. three different letters and one digit,[3]
4. exactly two letters and two digits, such that the letters are the same or the digits are the same, but not both.[3]