A five digit number is formed using digits 1, 3, 5, 7 and 9 without repeating any one of them

A five digit number is formed using digits 1, 3, 5, 7 and 9 without repeating any one of them. What is the sum of all such possible numbers?

  1. 6666666
  2. 6666600
  3. 6666660
  4. 6666000

Answer

If you assume that any digit is in fixed position, then the remaining four digits can be arranged in 4! = 24 ways.

So, each of the 5 digit will appear in each of the five places 24 times. So, the sum of the digits in each position is 24(1+3+5+7+9) = 600

The sum of all such numbers will be 600(1 + 10 + 100 + 1000 + 10000) = 6666600

The correct option is B.