2022 NYJC P2 Q6

Jean has forgotten the six-character login password for her laptop. She remembers that the password consists of four distinct letters from the twenty-six letters of the alphabet A − Z and two distinct digits from the ten digits \(0-9\).

1. Assuming that Jean keys in a six-character password for all her login attempts and she never repeats the same incorrect password, find the largest number of unsuccessful login attempts.[2]
2. Find the number of possible six-character passwords if the first four characters are distinct letters in alphabetical order.[2]
3. Given that the first four characters are distinct letters, and the last two characters are distinct digits, find the probability that exactly one of the four letters is a vowel.[3]