A five digit number is formed using the digits 1, 3, 5, 7, 9 without repeating any of them. What is the sum of all such possible five digit numbers?
A. 6666600 B. 6666600 C. 0000000 D. 0000000
GATE 2014 · General Aptitude · Combinatorics · medium
Answer: 6,666,600 (option B)
Count total permutations and frequency per position: Total numbers = 5! = 120. By symmetry, each digit appears in each position 120/5 = 4! = 24 times.
Sum of the 5 digits: Sum of digits = 1 + 3 + 5 + 7 + 9 = 25.
Sum of place values (repunit): Place values: 1 + 10 + 100 + 1000 + 10000 = 11111.
Compute total sum: Sum = 24 x 25 x 11111 = 600 x 11111 = 6,666,600.