Question

Four digit numbers are formed using \( 0, 3, 4, 5, 9, 8 \) without repetitions. Then the number of such 4 digit numbers is

• A. \( 270 \)
• B. \( 300 \)
• C. \( 320 \)
• D. \( 400 \)
• E. \( 450 \)

Hint:

Whenever digits include \( 0 \), always handle the first digit separately in number formation questions, because a number cannot start with zero.

Answer 1

The Correct Option is B

To find the number of 4-digit numbers that can be formed using the digits \(0, 3, 4, 5, 9, 8\) without repetitions, we proceed by considering the restrictions on selecting the first digit of the number.

1. Choosing the first digit:
   • The first digit cannot be 0 since it needs to be a 4-digit number. Therefore, we have five choices for the first digit: \(3, 4, 5, 9,\) or \(8\).
2. Choosing the other three digits:
   • Once we have selected the first digit, we cannot use it again. Thus, we have 5 remaining digits to choose from for the second position, 4 for the third position, and 3 for the fourth position.

Total number of 4-digit numbers:

Thus, the total number of such 4-digit numbers is: \(5 \times 60 = 300\).

Conclusion: The total number of 4-digit numbers that can be formed using the digits \(0, 3, 4, 5, 9, 8\) without repetition is 300. Therefore, the correct option is \( \boxed{300} \).