Mathematics
Mathematics
Problem
A user ID is to be created with a sequence of three distinct letters chosen from followed by a two-digit number. The second letter in the sequence must not be a vowel, and the two digits must be distinct with the last digit odd. How many different user IDs can be formed? a) b) c) d)Intuitive explanation
The key is to break this into independent stages and count carefully at each step. First, you'll arrange three distinct letters with a constraint on the middle position—identify which letters are vowels and which aren't, then count valid letter sequences. Next, form a two-digit number where the digits differ and the last one is odd, which means you pick an odd digit first, then choose a different digit for the tens place. Multiply the counts together since each choice stage is independent.
Intuitive explanation
The key is to break this into independent stages and count carefully at each step. First, you'll arrange three distinct letters with a constraint on the middle position—identify which letters are vowels and which aren't, then count valid letter sequences. Next, form a two-digit number where the digits differ and the last one is odd, which means you pick an odd digit first, then choose a different digit for the tens place. Multiply the counts together since each choice stage is independent.