How many four-digit odd numbers less than 6000 can be formed using the digits 2, 4, 6, 7, 8, and 9?

Key Concepts

Four-Digit Numbers

A four-digit number is a number that has exactly four digits, ranging from 1000 to 9999. In this context, we are interested in forming four-digit numbers using specific digits while adhering to certain conditions, such as being odd and less than 6000.

Odd Numbers

An odd number is an integer that is not divisible by 2, which means its last digit must be one of the odd digits. In this case, the available odd digits from the set {2, 4, 6, 7, 8, 9} are 7 and 9, which will determine the last digit of the four-digit number.

Permutations with Restrictions

When forming numbers from a set of digits, permutations refer to the different arrangements of those digits. In this problem, we must consider restrictions such as the number being less than 6000 and using only the specified digits, which affects how we can arrange the first three digits of the number.