How many four-digit odd numbers less than 4000 can be formed using the digits 2, 3, 4, 5, 6, and 8?

To find how many four-digit odd numbers less than 4000 can be formed using the digits 2, 3, 4, 5, 6, and 8, let's follow these steps:

Understanding the conditions : The number must be odd and less than 4000. The digits available are 2, 3, 4, 5, 6, and 8.

Determining constraints :

Odd number : To be odd, the last digit of the number must be either 3 or 5 (since these are the only odd digits available).
Less than 4000 : The first digit must be less than 4. Thus, the possible choices for the first digit are 2 or 3.


Choosing the last digit :

First, let's determine how many numbers have 3 as the last digit:
First digit : 2 or 3 (2 choices).
Second and Third digits : These can be filled with any of the remaining 4 digits from the set {2, 3, 4, 5, 6, 8}, chosen in any order, giving us 4 choices for the second digit and 3 choices for the third digit.



Calculating these permutations: 2 (choices for first digit) × 4 (choices for second digit) × 3 (choices for third digit) = 24 numbers with 3 as the last digit

Choosing the last digit as 5 :

Similarly, when 5 is the last digit:
First digit : 2 or 3 (2 choices).
Second and Third digits : Again, these can be filled with any 4 remaining digits, giving us 4 choices for the second digit and 3 choices for the third digit.



Calculating these permutations: 2 × 4 × 3 = 24 numbers with 5 as the last digit

Summing it all up : By adding the numbers formed by using either 3 or 5 as the last digit:
24 + 24 = 48


Therefore, there are a total of 48 four-digit odd numbers less than 4000 that can be formed using the digits 2, 3, 4, 5, 6, and 8.

Answered by BenjaminOwenLewis | 2025-07-21