2025 VJC P2 Q5

A code consists of \(10\) characters.

The first \(5\) characters of the code is formed using \(5\) letters chosen from the set \(\{A, B, C, D, E, F, G, H\}\) and the last \(5\) characters of the code is formed using \(5\) digits chosen from the set \(\{1, 2, 3, 4, 5, 6, 7, 8, 9, 0\}\). The code allows for repetitions of letters and/or digits.

1. Find the number of different codes that can be formed.[1]
2. Find the probability that a code chosen at random
   1. contains the letter \(E\) exactly thrice and the number \(5\) exactly once,[2]
   2. has \(E\) as the first character or \(4\) as its tenth character, but not both.[2]