Question:
Four digit numbers are formed using \( 0, 3, 4, 5, 9, 8 \) without repetitions. Then the number of such 4 digit numbers is
Four digit numbers are formed using \( 0, 3, 4, 5, 9, 8 \) without repetitions. Then the number of such 4 digit numbers is
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Whenever digits include \( 0 \), always handle the first digit separately in number formation questions, because a number cannot start with zero.
Updated On: Apr 28, 2026
- \( 270 \)
- \( 300 \)
- \( 320 \)
- \( 400 \)
- \( 450 \)
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The Correct Option is B
Solution and Explanation
Step 1: Identify the given digits.
The digits available are: \[ 0, 3, 4, 5, 8, 9 \] So, total number of distinct digits is \( 6 \).
We have to form \( 4 \)-digit numbers without repetition.
Step 2: Recall the restriction for a 4-digit number.
A \( 4 \)-digit number cannot begin with \( 0 \), because if the first digit is \( 0 \), the number will not remain a 4-digit number.
So, the first place must be filled only by one of the non-zero digits: \[ 3, 4, 5, 8, 9 \] Hence, the first digit can be chosen in \[ 5 \text{ ways} \]
Step 3: Choose the second digit.
After choosing the first digit, one digit is already used.
Out of the original \( 6 \) digits, \( 5 \) digits remain available for the second position.
Since repetition is not allowed, the second digit can be chosen in \[ 5 \text{ ways} \]
Step 4: Choose the third digit.
Now two digits have already been used.
So, the number of remaining digits is \[ 6-2=4 \] Thus, the third digit can be selected in \[ 4 \text{ ways} \]
Step 5: Choose the fourth digit.
Now three digits are already occupied.
So, the number of remaining digits is \[ 6-3=3 \] Hence, the fourth digit can be selected in \[ 3 \text{ ways} \]
Step 6: Apply the multiplication principle.
By the fundamental principle of counting, the total number of 4-digit numbers is \[ 5 \times 5 \times 4 \times 3 \] \[ =25 \times 12 \] \[ =300 \]
Step 7: Final conclusion.
Therefore, the total number of 4-digit numbers that can be formed is \[ \boxed{300} \] Hence, the correct option is \[ \boxed{(2)\ 300} \]
The digits available are: \[ 0, 3, 4, 5, 8, 9 \] So, total number of distinct digits is \( 6 \).
We have to form \( 4 \)-digit numbers without repetition.
Step 2: Recall the restriction for a 4-digit number.
A \( 4 \)-digit number cannot begin with \( 0 \), because if the first digit is \( 0 \), the number will not remain a 4-digit number.
So, the first place must be filled only by one of the non-zero digits: \[ 3, 4, 5, 8, 9 \] Hence, the first digit can be chosen in \[ 5 \text{ ways} \]
Step 3: Choose the second digit.
After choosing the first digit, one digit is already used.
Out of the original \( 6 \) digits, \( 5 \) digits remain available for the second position.
Since repetition is not allowed, the second digit can be chosen in \[ 5 \text{ ways} \]
Step 4: Choose the third digit.
Now two digits have already been used.
So, the number of remaining digits is \[ 6-2=4 \] Thus, the third digit can be selected in \[ 4 \text{ ways} \]
Step 5: Choose the fourth digit.
Now three digits are already occupied.
So, the number of remaining digits is \[ 6-3=3 \] Hence, the fourth digit can be selected in \[ 3 \text{ ways} \]
Step 6: Apply the multiplication principle.
By the fundamental principle of counting, the total number of 4-digit numbers is \[ 5 \times 5 \times 4 \times 3 \] \[ =25 \times 12 \] \[ =300 \]
Step 7: Final conclusion.
Therefore, the total number of 4-digit numbers that can be formed is \[ \boxed{300} \] Hence, the correct option is \[ \boxed{(2)\ 300} \]
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