Number of 5-digit numbers can be formed using the digits 2,4,7,9,0 if no digit is repeated :

Options

A. 69
B. 96
C. 169
D. 98

Answer

To find the number of 5-digit numbers that can be formed using the digits 2, 4, 7, 9, and 0 without repeating any digit, we can follow these steps:

### Step 1: Identify the digits
The available digits are 2, 4, 7, 9, and 0.

### Step 2: Determine the first digit
The first digit of a 5-digit number cannot be 0 (as it would then be a 4-digit number). Therefore, the possible choices for the first digit are 2, 4, 7, or 9. This gives us 4 options for the first digit.

### Step 3: Determine the second digit
Once the first digit is chosen, we cannot use that digit again. Since we started with 5 digits and have used 1, we have 4 remaining digits. Therefore, we have 4 options for the second digit.

### Step 4: Determine the third digit
After selecting the first and second digits, we will have used 2 digits, leaving us with 3 remaining digits. Thus, we have 3 options for the third digit.

### Step 5: Determine the fourth digit
Similarly, after choosing the first three digits, we will have used 3 digits, leaving us with 2 remaining digits. Therefore, we have 2 options for the fourth digit.

### Step 6: Determine the fifth digit
Finally, after selecting the first four digits, we will have used 4 digits, leaving us with only 1 digit remaining. Thus, we have 1 option for the fifth digit.

### Step 7: Calculate the total number of combinations
Now, we can multiply the number of options for each digit:
- Options for the first digit: 4
- Options for the second digit: 4
- Options for the third digit: 3
- Options for the fourth digit: 2
- Options for the fifth digit: 1

So, the total number of 5-digit numbers is:
\[ 4 \times 4 \times 3 \times 2 \times 1 = 96 \]

### Final Answer
The total number of 5-digit numbers that can be formed is **96**.

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