How many number of 5 digits can be formed with the digits 0,2,4,6,8 if repetition of digits is not allowed?

Options

A. `120`
B. `3125`
C. `96`
D. `24`

Explanation

To solve the problem of how many 5-digit numbers can be formed using the digits 0, 2, 4, 6, and 8 without repetition, we can follow these steps:

### Step 1: Identify the digits available
The available digits are 0, 2, 4, 6, and 8.

### Step 2: Determine the first digit
Since we are forming a 5-digit number, the first digit cannot be 0 (as it would then be a 4-digit number). Therefore, the possible choices for the first digit are 2, 4, 6, or 8. This gives us **4 choices** for the first digit.

### Step 3: Determine the remaining digits
After selecting the first digit, we have used one digit, leaving us with 4 digits remaining (including 0).

### Step 4: Fill the second digit
For the second digit, we can use any of the remaining 4 digits (including 0). Thus, we have **4 choices** for the second digit.

### Step 5: Fill the third digit
After choosing the first and second digits, we have used 2 digits, leaving us with 3 digits remaining. Therefore, we have **3 choices** for the third digit.

### Step 6: Fill the fourth digit
After choosing the first three digits, we have used 3 digits, leaving us with 2 digits remaining. Thus, we have **2 choices** for the fourth digit.

### Step 7: Fill the fifth digit
Finally, after choosing the first four digits, we have used 4 digits, leaving us with 1 digit remaining. Therefore, we have **1 choice** for the fifth digit.

### Step 8: Calculate the total number of combinations
Now, we multiply the number of choices for each digit position:
\[ \text{Total combinations} = 4 \times 4 \times 3 \times 2 \times 1 = 96 \]

Thus, the total number of 5-digit numbers that can be formed is **96**.

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