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InterviewSolution
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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? |
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Answer» 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. 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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