find number of ways of 3 digit number that can be formed using the digits 0,1,2,3,4 without repetition of numbers

To form a 3-digit number using the digits \(0, 1, 2, 3, 4\) without repetition, we must consider the following:

### Step 1: First Digit (Hundreds Place)
The first digit of a 3-digit number cannot be \(0\), as that would make it a 2-digit number. So, the choices for the first digit are \(1, 2, 3, 4\) (4 choices).

### Step 2: Second Digit (Tens Place)
Once the first digit is chosen, we have 4 remaining digits available. Since repetition is not allowed, the number of choices for the second digit is now reduced to 4.

### Step 3: Third Digit (Units Place)
After selecting the first two digits, we are left with 3 unused digits. Therefore, we have 3 choices for the third digit.

### Step 4: Total Number of Combinations
The total number of 3-digit numbers is the product of the choices available for each place:

\[
\text{Total Ways} = 4 \times 4 \times 3 = 48
\]

Thus, the total number of 3-digit numbers that can be formed using the digits \(0, 1, 2, 3, 4\) without repetition is **48**.

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Here are 5 related questions to expand on this topic:
1. How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4 without repetition?
2. What is the total number of ways to arrange all the digits \(0, 1, 2, 3, 4\) into a 5-digit number?
3. How many 3-digit numbers can be formed using only even digits from \(0, 1, 2, 3, 4\)?
4. If repetition were allowed, how many 3-digit numbers could be formed from \(0, 1, 2, 3, 4\)?
5. What is the probability of forming a 3-digit number divisible by 5 using the digits \(0, 1, 2, 3, 4\) without repetition?

**Tip:** When dealing with digit problems, always pay attention to whether repetition is allowed or not, as it greatly impacts the total number of possibilities.

Explore the solution to finding how many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4 without repetition. Learn about combinatorics and permutation concepts for students in Grades 5-7, with detailed steps and formulas.

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