Question

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

• A. $9\times {10}^4$
• B. $\frac{9\times {10}^4}{2}$
• C. ${10}^5$
• D. none of these

Answer 1

Answer: (B)

$\frac{9\times {10}^4}{2}$

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

$5$ Digit number

If sum of first $4$ digits is even then last digit should be odd and if it is odd then it should be even $=5$ Ways

Total numbers

$=9\times 10\times 10\times 10\times 5=4.5\times {10}^4=\frac{9}{2}\times {10}^4$

Hence the correct answer is $\frac{9}{2}\times {10}^4$