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How many three digit numbers are there such that the sum of whose digits is odd?


The answer is 450.

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1 solution

Abhay Tiwari
Apr 19, 2016

Sum of the three digit will be odd only if

  • all the three digits are odd.
  • only one digit odd, rest two are even.

Now,

Digits with all odd number w i t h r e p e t i t i o n with repetition will be: 5 × 5 × 5 = 125 \boxed{5}×\boxed{5}×\boxed{5}= \boxed{125}

Numbers with one odd and two even:

  • 1) e v e n e v e n o d d \boxed{even} \boxed{even}\boxed{odd}

Total cases 4 × 5 × 5 = 100 4×5×5=\boxed{100}

  • 2) e v e n o d d e v e n \boxed{even} \boxed{odd}\boxed{even}

Total cases 4 × 5 × 5 = 100 4×5×5=\boxed{100}

  • 3) o d d e v e n e v e n \boxed{odd} \boxed{even}\boxed{even}

Total cases 5 × 5 × 5 = 125 5×5×5=\boxed{125}

Which brings the total to 125 + 100 + 100 + 125 = 450 125+100+100+125=\boxed{450}

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