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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?

1. 6666660
2. 6666600
3. 6666666
4. 6666606

Correct answer: 6666600

Solution

There are $5!=120$ such numbers. Each digit appears $(4!)=24$ times in each place. The sum of digits is $1+3+5+7+9=25$, so the total sum is $24\times 25\times 11111=6,666,600$.

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