The sum of all 3-digit numbers whose digits are all odd is ?

1 Answer
Jun 26, 2018

#69375#

Explanation:

  • The only odd digits are #1, 3, 5, 7, 9#, all of which are non-zero.

  • The number of ways of forming a three digit number from these digits is #5^3 = 125#, since there are #5# choices for the first digit, #5# for the second, and #5# for the third.

  • In these #125# ways, each digit has the same frequency.

  • The average digit value is #1/5(1+3+5+7+9) = 5#.

  • Each possible three digit number is a linear combination of digits.

  • Hence the average value of one of the three digit numbers is #555#.

So the sum is:

#5^3 * 555 = 125 * 555 = 69375#