Question

The sum of $5$ digit numbers such that the sum of their digit is even is :

• A. $50000$
• B. $45000$
• C. $60000$
• D. none

Answer 1

The correct option is B $45000$

The first digit can be chosen in 9 ways (excluding 0)

the second digit can be chosen in 10 ways.

third digit can be chosen in 10 ways.

fourth digit can be chosen in 10 ways.

Now the fifth digit can be chosen in 5 ways.

because if the sum of four-digit is even then

fifth digit can be chosen in 5 ways even OR

if the sum of four digits is odd then

also, the fifth digit can be chosen in 5 ways

$\therefore$ Total number of digit = $9\times 10\times 10\times 10\times 5=45000$