# Questionbank: Permutation and Probability

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Clue - FInd the number of rearrangements and then focus on the number of digits

## Sum of Rearrangements

Q.26: What is sum of all rearrangements of the 4-digit number 3214?
1. 66660
2. 55554
3. 60048
4. 65024

Choice A. 66660

## Detailed Solution

Total number of rearrangements = 4! Ways = 24.

Each of the four digits is likely to appear in the units place , therefore - ${7 \over 10}$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.

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