Question

How many different six-digit numbers are there the sum of whose digits is odd?

Answer 1

Half of them have odd sum$.$ If the first $5$ digit have as odd sum$,$ having an even $6^{th}$ digit makes the result odd$.$ If the first $5$ have an even sum$,$ and odd $6^{th}$ digit makes the result odd$.$ Either way$,$ half the choices for the $6^{th}$ digit make the sum of digits odd$.$

So$,$ on counting total numbers $:$from $100000$ to $999999$ we get total 900000 numbers. Total number of six-digit numbers the sum of whose digits is oddis $450000.$