A code consists of $10$ characters. The first $5$ characters of the code is formed using $5$ l

Question

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

Accepted Answer

(a)3276800000 (b)(i)0.00491 (b)(ii)0.2

2025 VJC P2 Q5

2025 VJC P2 Q5