Problem: Find the sum of all the four-digit numbers that formed with the digits 3,2,3,4.

Solution:
To find the sum of all the four-digit numbers that can be formed by using the digits 3,2,3,4, we need to find all possible permutations of these digits and then add them up.

Step 1: Find the total number of four-digit numbers that can be formed using the digits 3,2,3,4
The number of permutations of n objects taken r at a time is given by nPr = n!/(n-r)!. In our case, we have 4 objects (3,2,3,4) and we need to find the number of permutations of these objects taken 4 at a time. So, the number of four-digit numbers that can be formed using these digits is given by:
4P4 = 4!/(4-4)! = 4! = 24

Step 2: Find the sum of all possible four-digit numbers
To find the sum of all possible four-digit numbers, we need to first find the sum of each digit in each place value. There are 24 different permutations of the digits, so we need to find the sum of each permutation and then add them up to get the total sum.

For example, the permutation 3,2,3,4 can form the following four-digit numbers:
- 3234
- 3243
- 3324
- 3342
- 3423
- 3432
- 2324
- 2342
- 2234
- 2243
- 2433
- 2443
- 4332
- 4323
- 4233
- 4243
- 3422
- 3433
- 3242
- 3233
- 2323
- 2332
- 2432
- 2442

To find the sum of each permutation, we can add up the digits in each place value. For example, for the number 3234, the sum of the digits in each place value is:
- Thousands place: 3
- Hundreds place: 2
- Tens place: 3
- Ones place: 4
So, the sum of the digits in 3234 is 3+2+3+4 = 12.

We can repeat this process for all 24 permutations and then add up the sums to get the total sum of all possible four-digit numbers.

Step 3: Calculate the total sum
After finding the sum of each permutation, we add them up to get the total sum:
12+13+12+14+12+12+11+9+9+9+12+13+12+12+12+13+11+10+11+11+10+10+11+12 = 279

Therefore, the sum of all the four-digit numbers that can be formed using the digits 3,2,3,4 is 279.

Answer: Option (c) 33963 is not correct. The correct answer is (b) 39996.