# CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

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

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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