How Many Four-Digit Numbers Can Be Formed?
When it comes to creating four-digit numbers, there are certain rules and conditions that need to be followed. The number of four-digit numbers that can be formed depends on the choices available for each digit in the number. In this article, we will explore how to calculate the number of four-digit numbers that can be formed under different conditions.
What is a Four-Digit Number?
A four-digit number is a number that consists of four digits, where the first digit cannot be zero (as a number like 0123 is not a valid four-digit number). The number can be any integer between 1000 and 9999, inclusive.
For example:
- 1023 is a valid four-digit number.
- 0001 is not a valid four-digit number, as it’s considered a one-digit number.
How to Calculate the Number of Four-Digit Numbers
1. Using Digits from 0 to 9
In general, a four-digit number can be formed by selecting digits for each of the four places:
- First digit (thousands place): The first digit must be any digit from 1 to 9 (it cannot be zero). Therefore, there are 9 possible choices for the first digit.
- Second digit (hundreds place): The second digit can be any digit from 0 to 9. Therefore, there are 10 possible choices for the second digit.
- Third digit (tens place): The third digit can also be any digit from 0 to 9. So, there are 10 possible choices for the third digit.
- Fourth digit (ones place): The fourth digit can be any digit from 0 to 9. Again, there are 10 possible choices for the fourth digit.
Thus, the total number of four-digit numbers that can be formed is the product of the choices for each digit: Total number of four-digit numbers=9×10×10×10=9,000\text{Total number of four-digit numbers} = 9 \times 10 \times 10 \times 10 = 9,000
Conclusion
There are 9,000 different four-digit numbers that can be formed using digits from 0 to 9, where the first digit is non-zero.
Summary of Key Points:
- The first digit can be any digit from 1 to 9 (9 choices).
- The second, third, and fourth digits can each be any digit from 0 to 9 (10 choices for each).
- The total number of four-digit numbers is 9,000.
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