# How many numbers can be formed less than 30000 can be formed by using 0,1,2,3,4,5?

How many numbers can be formed less than 30000 can be formed by using 0,1,2,3,4,5?

#### kvishal9956

##### New member
1. Numbers with 1 digit: There are 6 single-digit numbers (0, 1, 2, 3, 4, 5) less than 30000.
2. Numbers with 2 digits: There are 5 choices for the first digit (1, 2, 3, 4, 5) and 6 choices for the second digit (0, 1, 2, 3, 4, 5). So, there are 5 * 6 = 30 two-digit numbers less than 30000.
3. Numbers with 3 digits: There are 5 choices for the first digit (1, 2, 3, 4, 5) and 6 choices for the second and third digits (0, 1, 2, 3, 4, 5). So, there are 5 * 6 * 6 = 180 three-digit numbers less than 30000.
4. Numbers with 4 digits: There are 5 choices for the first digit (1, 2, 3, 4, 5) and 6 choices for the other digits. So, there are 5 * 6 * 6 * 6 = 1080 four-digit numbers less than 30000.
5. Numbers with 5 digits: There are 2 choices for the first digit (1, 2) and 6 choices for the other digits. So, there are 2 * 6 * 6 * 6 * 6 = 2592 five-digit numbers less than 30000.
Adding up the numbers from all the cases:

Total numbers less than 30000 = 6 (1-digit) + 30 (2-digit) + 180 (3-digit) + 1080 (4-digit) + 2592 (5-digit) = 3888.(assuming repetition is allowed)