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?

- 66660
- 55554
- 60048
- 65024

66660

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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?"**

Choice A is the correct answer.

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