The sum of all 3-digit numbers whose digits are all odd is ?
1 Answer
Jun 26, 2018
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#