Sum of specific 4-digit permutations

We need to form 4-digit numbers using \{1, 2, 3, 4\} without repetition, such that the values are less than 2000. This constraint forces the thousands digit to be exactly 1.

The remaining slots (hundreds, tens, units) must be a permutation of the numbers \{2, 3, 4\}. There are 3! = 6 such numbers in total. In these 6 numbers, each remaining digit \{2, 3, 4\} appears exactly 6 \div 3 = 2 times in the hundreds, tens, and units positions.

Sum of digits for each trailing column = 2 × (2 + 3 + 4) = 2 × 9 = 18. Apply column place-values to calculate the final sum:

Total Grand Sum = 6000 + 1800 + 180 + 18 = 7998.

Answer: (a).