How many 3-digit combinations are there?

Understand the Problem

The question is asking for the total number of three-digit combinations that can be formed, which typically involves understanding permutations and the arrangement of digits.

Answer

The total number of three-digit combinations is \(900\).

Steps to Solve

Identify the range of digits Three-digit combinations can be formed using digits from 0 to 9. However, since we are considering three-digit numbers, the first digit cannot be 0. Therefore, we have the choices for the first digit.
Calculate choices for the first digit For the first digit, we can choose from 1 to 9 (9 options) because we cannot have a leading zero as part of a three-digit number.
Calculate choices for the second digit For the second digit, we can choose any digit from 0 to 9 (10 options).
Calculate choices for the third digit Similar to the second digit, the third digit can also be any digit from 0 to 9 (10 options).
Calculate the total combinations Now, we multiply the number of options for each digit:

[ \text{Total combinations} = (\text{choices for first digit}) \times (\text{choices for second digit}) \times (\text{choices for third digit}) = 9 \times 10 \times 10 ]

Perform the multiplication to find the total number of three-digit combinations.

The total number of three-digit combinations is (900).

More Information

In total, there are 900 unique combinations of three-digit numbers ranging from 100 to 999, inclusive. This shows how many different numbers can be formed with three digits while adhering to the rule that the first digit cannot be zero.

Tips

Ignoring leading zero restriction: A common mistake is to include the digit 0 as an option for the first digit, which is not allowed in three-digit numbers. Always ensure the first digit is between 1 and 9.
Miscalculating the total: Ensure that you are multiplying the numbers of options accurately for each digit.

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