N2013 P2 Q11

A machine is used to generate codes consisting of three letters followed by two digits. Each of the three letters generated is equally likely to be any of the twenty-six letters of the alphabet A – Z. Each of the two digits generated is equally likely to be any of the nine digits \(1-9\). The digit \(0\) is not used.

Find the probability that a randomly generated chosen code has

1. three different letters and two different digits,[2]
2. the second digit is higher than the first digit,[2]
3. exactly two letters the same or two digits the same, but not both,[4]
4. exactly one vowel (A, E, I, O or U) and exactly one even digit.[4]