correct answer is: b) 1998

Explanation

To find the sum of all three digits numbers that can be formed using the digits 2, 3, and 4 without repetition, we can first count how many such numbers create and then calculate their sum.
\rightarrow We have 3 choices for the hundreds place (2,3 or 4)
\rightarrow Once we have chosen one digit for the hundreds place, we have 2 remaining choices for the tens place.
\rightarrow After choosing digits for the hundreds and tens places, only 1 digit remains for the unit’s place.
\therefore We can form \left(3\times2\times1\right)=6 possible numbers.
So that, these numbers are : 234, 243, 324, 342, 423 and 432.
\therefore Their sum is : (234+243+324+342+423+432)
\rightarrow 1998
Ans: The sum of all three digits numbers formed with the digits 2, 3 and 4, without repeating any digit, is 1998.

This particular math question can also be formulated in the following manner:

1. How to find the sum of all three digit numbers formed by the digits 2, 3, and 4, ensuring each digit appears only once?
2. Finding the total value of three digit numbers formed by the digits 2, 3, and 4, without repeating any digit.
3. How to calculate the sum of all unique three digit numbers using the digits 2, 3, and 4, with no repetition?