# CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

###### CAT Questions | Permutation Probability | Sum of Rearrangements

The question is from Permutation and Combination. This question is about Sum of Rearrangements. We need to find out the sum of all possible numbers when a four digit number is rearranged. This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 26: What is sum of all rearrangements of the 4-digit number 3214?

1. 66660
2. 55554
3. 60048
4. 65024

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##### Method of solving this CAT Question from Permutation and Combination: Clue - FInd the number of rearrangements and then focus on the number of digits

Total number of rearrangements = 4! Ways = 24.
Each of the four digits is likely to appear in the units place , therefore - $$frac{7}{10}\\$th of 24 = 6 numbers will have 2 in the units place, 6 will have 1 in the units place and so on.. Therefore, sum of units place = 6*$2+3+1+4) = 60
Sum of tens place = 6*(20+30+10+40) = 600.
Sum of hundreds place = 6*1000 =6000
Sum of thousands place = 6*10000 =60000. Therefore, sum of all rearrangements of 3214 = 66660.

The question is "What is sum of all rearrangements of the 4-digit number 3214?"

##### Hence the answer is "66660"

Choice A is the correct answer.

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