How many different numbers of 3 digits can be formed with the digits ,1,2,4,5,7,8, none of the digits being repeated in any of the numbers so formed ?

Options

A. 120
B. 1200
C. 180
D. 270

Answer

To solve the problem of how many different 3-digit numbers can be formed using the digits 1, 2, 4, 5, 7, and 8 without repeating any digits, we can follow these steps:

### Step 1: Identify the total number of available digits
We have the digits: 1, 2, 4, 5, 7, and 8. This gives us a total of 6 digits.

### Step 2: Determine the number of choices for the first digit
For the first digit of the 3-digit number, we can choose any of the 6 digits. Therefore, there are 6 options for the first digit.

### Step 3: Determine the number of choices for the second digit
Once we have chosen the first digit, we cannot use that digit again. This leaves us with 5 remaining digits to choose from for the second digit. Thus, there are 5 options for the second digit.

### Step 4: Determine the number of choices for the third digit
After selecting the first and second digits, we will have used 2 digits, leaving us with 4 digits left to choose from for the third digit. Therefore, there are 4 options for the third digit.

### Step 5: Calculate the total number of different 3-digit numbers
To find the total number of different 3-digit numbers that can be formed, we multiply the number of choices for each digit together:

\[ \text{Total Numbers} = (\text{Choices for 1st digit}) \times (\text{Choices for 2nd digit}) \times (\text{Choices for 3rd digit}) = 6 \times 5 \times 4 \]

Calculating this gives:

\[ 6 \times 5 = 30 \]
\[ 30 \times 4 = 120 \]

So, the total number of different 3-digit numbers that can be formed is **120**.

### Final Answer
The total number of different 3-digit numbers that can be formed is **120**.

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