Arithmetic Ability
Permutations and Combinations

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Q.

Compute the sum of 4 digit numbers which can be formed with the four digits 1,3,5,7, if each digit is used only once in each arrangement.

View Answer

Correct choice: C

Explanation:

The number of arrangements of 4 different digits taken 4 at a time is given by 4P4 = 4! = 24.All the four digits will occur equal number of times at each of the position,namely ones,tens,hundreds,thousands. Thus,each digit will occur 24/4 = 6 times in each of the position.The sum of digits in one's position will be 6 x (1+3+5+7) = 96.Similar is the case in ten's,hundred's and thousand's places. Therefore,the sum will be 96 + 96 x 10 + 96 x 100 + 96 x 100 = 106656
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