Permutations & Combinations
Sum of All 4-digit Numbers with Repeated Digits
nta_pyq_2023_apr
Grade 11
Question:
Sum of all 4-digit numbers using digits 2,1,2,3 (all used) is equal to ____.
Step-by-Step Solution
Key Concept: Total arrangements $=\frac{4!}{2!}=12$. Each digit appears $\frac{12}{4}\times2=6$ times for 2, and $3$ times each for 1,3. Sum $=3\times(1111)(1+3)+6\times(1111)\times2$.
$1111\times24=26664$.
Correct Answer: 26664