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

To determine how many numbers less than 30,000 can be formed using the digits 0, 1, 2, 3, 4, and 5, we need to consider the constraints imposed by the maximum value and the rules of number formation. Since we are looking for numbers less than 30,000, we can have numbers with 1, 2, 3, 4, or 5 digits. Let's break this down step by step.

1-Digit Numbers

The only valid 1-digit numbers we can form using the digits 0, 1, 2, 3, 4, and 5 are 1, 2, 3, 4, and 5. The digit 0 cannot be used as a standalone number.

• Count: 5

2-Digit Numbers

For 2-digit numbers, the first digit cannot be 0. Therefore, the first digit can be 1, 2, 3, 4, or 5 (5 options), and the second digit can be any of the 6 digits (0, 1, 2, 3, 4, 5).

• First digit: 5 options (1-5)
• Second digit: 6 options (0-5)
• Total: 5 × 6 = 30

3-Digit Numbers

For 3-digit numbers, again the first digit cannot be 0. The first digit has 5 options (1-5), while the second and third digits can each be any of the 6 digits.

• First digit: 5 options (1-5)
• Second digit: 6 options (0-5)
• Third digit: 6 options (0-5)
• Total: 5 × 6 × 6 = 180

4-Digit Numbers

For 4-digit numbers, the first digit again cannot be 0. The first digit has 5 options, while the other three digits can be any of the 6 digits.

• First digit: 5 options (1-5)
• Second digit: 6 options (0-5)
• Third digit: 6 options (0-5)
• Fourth digit: 6 options (0-5)
• Total: 5 × 6 × 6 × 6 = 1080

5-Digit Numbers

For 5-digit numbers, the first digit can be 1 or 2 (since we want numbers less than 30,000). If the first digit is 1 or 2, the remaining four digits can be any of the 6 digits.

• First digit: 2 options (1 or 2)
• Second digit: 6 options (0-5)
• Third digit: 6 options (0-5)
• Fourth digit: 6 options (0-5)
• Fifth digit: 6 options (0-5)
• Total: 2 × 6 × 6 × 6 × 6 = 2592

Final Calculation

Now, let's sum all the possibilities:

• 1-digit: 5
• 2-digit: 30
• 3-digit: 180
• 4-digit: 1080
• 5-digit: 2592

Total numbers less than 30,000: 5 + 30 + 180 + 1080 + 2592 = 3887

In conclusion, a total of 3,887 different numbers can be formed using the digits 0, 1, 2, 3, 4, and 5 that are less than 30,000.