Question

The sum of all the four-digit numbers that can be formed using all the digits 2, 1, 2, 3 is equal to ______.

Answer 1

The number of four-digit numbers that can be formed using the digits 2, 1, 2, and 3 is \( \frac{4!}{2!} = 12 \). 
These are the permutations of the digits 2, 1, 2, and 3. The sum of digits at the unit place is calculated as: \[ 3 \times 1 + 6 \times 2 + 3 \times 3 = 24. \] Now, the required sum is: \[ 24 \times 1000 + 24 \times 100 + 24 \times 10 + 24 \times 1 = 24 \times (1000 + 100 + 10 + 1) = 24 \times 1111 = 26664. \] Thus, the sum is \( 26664 \).