Question

How many 5-digit numbers can be formed with the digits 0, 1, 2, 3, 4, with no digit being repeated?

• A. 120
• B. 24
• C. 96
• D. 5

Hint:

When forming a number with no repetition of digits, consider the restrictions on which digits can be used for each position, such as the first digit not being zero.

Answer 1

The Correct Option is C

We are asked to form a 5-digit number using the digits \( 0, 1, 2, 3, 4 \) with no repetition of digits.

Step-by-step Calculation:

1. Choosing the first digit:

The first digit cannot be \( 0 \) (as it would not form a valid 5-digit number). So, the first digit must be one of \( 1, 2, 3, 4 \). This gives us 4 choices for the first digit.

2. Choosing the second digit:

After choosing the first digit, we can choose the second digit from the remaining 4 digits (including 0).
Therefore, there are 4 choices for the second digit.

3. Choosing the third digit:

After choosing two digits, we have 3 digits left. So, there are 3 choices for the third digit.

4. Choosing the fourth digit:

After choosing three digits, we have 2 digits left. So, there are 2 choices for the fourth digit.

5. Choosing the fifth digit:

After choosing four digits, we have only 1 digit left. So, there is 1 choice for the fifth digit.

Total number of 5-digit numbers:

The total number of 5-digit numbers can be found by multiplying the number of choices for each digit:

\( 4 \times 4 \times 3 \times 2 \times 1 = 96 \)

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

Conclusion:

The number of 5-digit numbers that can be formed is 96.

Correct Answer:

96