GATE EC 2014 Set 4 — Question 10
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General Aptitude → Quantitative Aptitude → Permutations & Combinations
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Question
A five digit number is formed using the digits 1, 3, 5, 7 and 9 without repeating any of them. What is the sum of all such possible five digit numbers?
Correct answer
(B) 6666600
Solution
To find the sum of all possible 5-digit numbers formed using the digits without repetition:
1.Total numbers possible: Since there are 5 distinct digits, the total number of permutations is .
2.Frequency of each digit in each position: In the set of all 120 numbers, each digit will appear in each place (units, tens, hundreds, thousands, and ten-thousands) an equal number of times.
Frequency = times.3.Sum of the given digits: .
4.Sum of digits in any single position: Since each digit appears 24 times in any given position, the sum of digits in that position is .
5.Total Sum calculation: The total sum is the sum of the values contributed by each position:
Thus, the correct option is (B).Continue learning with Success Tracker
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