The number of 5-digit numbers that can be formed using the digits 3,4,5,6 and 7 without repetition is____.

Options

A. 120
B. 80
C. 150
D. 100

Answer

To find the number of 5-digit numbers that can be formed using the digits 3, 4, 5, 6, and 7 without repetition, we can follow these steps:

### Step 1: Identify the digits available
We have the digits: 3, 4, 5, 6, and 7. There are a total of 5 digits.

### Step 2: Determine the number of positions
Since we are forming a 5-digit number, we will have 5 positions to fill.

### Step 3: Calculate the number of ways to fill each position
- For the **first position**, we can choose any of the 5 digits (3, 4, 5, 6, 7). So, there are **5 choices**.
- For the **second position**, since we cannot repeat the digit used in the first position, we have **4 remaining choices**.
- For the **third position**, we will have **3 remaining choices** after filling the first two positions.
- For the **fourth position**, there will be **2 remaining choices**.
- For the **fifth position**, there will be **1 remaining choice**.

### Step 4: Multiply the number of choices for each position
The total number of ways to fill the 5 positions is calculated by multiplying the number of choices for each position:

\[ \text{Total ways} = 5 \times 4 \times 3 \times 2 \times 1 \]

### Step 5: Calculate the result
Now, we can calculate the total:

\[ 5 \times 4 = 20 \]
\[ 20 \times 3 = 60 \]
\[ 60 \times 2 = 120 \]
\[ 120 \times 1 = 120 \]

Thus, the total number of 5-digit numbers that can be formed is **120**.

### Final Answer
The number of 5-digit numbers that can be formed using the digits 3, 4, 5, 6, and 7 without repetition is **120**.

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