JEE MAIN - Mathematics (2023 - 10th April Evening Shift - No. 15)
The sum of all the four-digit numbers that can be formed using all the digits 2, 1, 2, 3 is equal to __________.
Answer
26664
Explanation
We have, four digits are $2,1,2,3$.
Total numbers when 1 is at unit digit $=\frac{3 !}{2 !}=3$
Total number when 2 is at unit digit $=3 !=6$
Total numbers when 3 is at unit digit $=\frac{3 !}{2 !}=3$
Sum of digits at unit place $=3 \times 1+6 \times 2+3 \times 3=24$
$\therefore$ Required sum $=24 \times 1000+24 \times 100+24 \times 10+24 \times 1$
$=24 \times 1111=26664$
Total numbers when 1 is at unit digit $=\frac{3 !}{2 !}=3$
Total number when 2 is at unit digit $=3 !=6$
Total numbers when 3 is at unit digit $=\frac{3 !}{2 !}=3$
Sum of digits at unit place $=3 \times 1+6 \times 2+3 \times 3=24$
$\therefore$ Required sum $=24 \times 1000+24 \times 100+24 \times 10+24 \times 1$
$=24 \times 1111=26664$
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