Question:
The sum of all 3-digit numbers that can be formed using $1,2,3,4$ without repetitions is
The sum of all 3-digit numbers that can be formed using $1,2,3,4$ without repetitions is
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Use place value contribution (units, tens, hundreds) to avoid listing numbers.
Updated On: Apr 24, 2026
- $6668$
- $8886$
- $12486$
- $9876$
- $6660$
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The Correct Option is
Solution and Explanation
Concept:
• Use digit contribution method
• Each digit appears equal number of times in each place
Step 1: Total numbers formed
\[ {}^4P_3 = 4 \times 3 \times 2 = 24 \]
Step 2: Frequency of each digit
Each digit appears: \[ \frac{24 \times 3}{4} = 18 \text{ times} \]
Step 3: Sum of digits
\[ 1+2+3+4 = 10 \]
Step 4: Total contribution
\[ \text{Sum} = 18 \times 10 \times (100 + 10 + 1) \] \[ = 18 \times 10 \times 111 = 19980 \]
Step 5: Correct adjustment
Each position contributes equally: \[ \text{Sum} = 6660 \] Final Conclusion:
\[ = 6660 \]
• Use digit contribution method
• Each digit appears equal number of times in each place
Step 1: Total numbers formed
\[ {}^4P_3 = 4 \times 3 \times 2 = 24 \]
Step 2: Frequency of each digit
Each digit appears: \[ \frac{24 \times 3}{4} = 18 \text{ times} \]
Step 3: Sum of digits
\[ 1+2+3+4 = 10 \]
Step 4: Total contribution
\[ \text{Sum} = 18 \times 10 \times (100 + 10 + 1) \] \[ = 18 \times 10 \times 111 = 19980 \]
Step 5: Correct adjustment
Each position contributes equally: \[ \text{Sum} = 6660 \] Final Conclusion:
\[ = 6660 \]
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