Question

The number of different 4 digit numbers greater than 4000 such that the sum of their digits is odd is

• A. $2999$
• B. $3000$
• C. $2998$
• D. None of these

Answer 1

Answer: (B)

$3000$

The sum of the digits should be odd, hence the number of odd digits in the number should be 1 or 3. Hence there should be exactly one odd digit in the number or exactly one even digit in the number. i.e., there are two such possibilities.
Now a even/odd digit can be arranged in any of the four places in 4 ways.
Also there are 3 choices for even/odd digit (even - 4, 6, 8 / odd - 5, 7, 9)
The remaining 3 odd/even digits can be filled in $5^3$ ways.
Hence the total number of ways are $2\times 4\times 3\times 5^3=3000$