The sum of all the 4 -digit distinct numbers

Question:

The sum of all the 4 -digit distinct numbers that can be formed with the digits $1,2,2$ and 3 is:

  1. (1) 26664

  2. (2) 122664

  3. (3) 122234

  4. (4) 22264


Correct Option: 1

Solution:

Digits are $1,2,2,3$

total distinct numbers $\frac{4 !}{2 !}=12$.

total numbers when 1 at unit place is 3 .

2 at unit place is 63 at unit place is 3 .

So, sum $=(3+12+9)\left(10^{3}+10^{2}+10+1\right)$

$=(1111) \times 24$

$=26664$

 

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