a) 1668

b) 1998

c) 2006

d) 2106

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:

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