Question

The total number of five digit numbers the sum of whose digits is even is

• A. $4.5\times {10}^4$
• B. $9\times {10}^4$
• C. ${10}^5$
• D. none of these

Answer 1

The correct option is A $4.5\times {10}^4$

$0,1,2,3,4,5,6,7,8,9$

Five digit number

Last digit can be filled in $5$ ways

That is if the first four digits add up to odd sum then last digit will be odd

Else it would be even

Total number of such digits

$=9\times 10\times 10\times 10\times 5=45\times {10}^3$

$=4.5\times {10}^4$

Hence, the correct answer is $4.5\times {10}^4$.