correct answer is: b) 1998

Explanation

To find the sum of all three digits numbers that can be formed using the digits KaTeX parse error: KaTeX doesn't work in quirks mode. and KaTeX parse error: KaTeX doesn't work in quirks mode. without repetition, we can first count how many such numbers create and then calculate their sum.
KaTeX parse error: KaTeX doesn't work in quirks mode. We have KaTeX parse error: KaTeX doesn't work in quirks mode. choices for the hundreds place KaTeX parse error: KaTeX doesn't work in quirks mode. or KaTeX parse error: KaTeX doesn't work in quirks mode.
KaTeX parse error: KaTeX doesn't work in quirks mode. Once we have chosen one digit for the hundreds place, we have KaTeX parse error: KaTeX doesn't work in quirks mode. remaining choices for the tens place.
KaTeX parse error: KaTeX doesn't work in quirks mode. After choosing digits for the hundreds and tens places, only KaTeX parse error: KaTeX doesn't work in quirks mode. digit remains for the unit’s place.
KaTeX parse error: KaTeX doesn't work in quirks mode. We can form KaTeX parse error: KaTeX doesn't work in quirks mode. possible numbers.
So that, these numbers areKaTeX parse error: KaTeX doesn't work in quirks mode.
KaTeX parse error: KaTeX doesn't work in quirks mode. Their sum isKaTeX parse error: KaTeX doesn't work in quirks mode.
KaTeX parse error: KaTeX doesn't work in quirks mode.
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?