using only odd digits, all possible three-digit numbers are formed.determine the sum of all such numbers ?

Question

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Answer 1

There are 5 odd digits, so there are 5^3 numbers with three odd digits.

That's 125 numbers, of which 1/5 will have 1 in the hundreds place (25 numbers in the 100s), 1/5 will have 3 (25 numbers in the 300s), 1/5 will have 5, etc.

So... the sum of all the hundreds digits would be
25*1 + 25*3 + 25*5 + 25*7 + 25*9 =
25*(1+3+5+7+9) =
25*25 =
625

The tens and ones digits are exactly the same (25 numbers with each of the 5 different digits), so the sum of all the numbers is 625 hundreds, 625 tens, and 625 ones:

62500 + 6250 + 625 =
69,375.