Question

The total number of three digit numbers, the sum of whose digits is even, is equal to

• A. $450$
• B. $350$
• C. $250$
• D. $325$

Answer 1

The correct option is A

$450$

Explanation of the correct option.

Let $n=pqr$ be the three digit number

So the sum of digits is $=p+q+r$

Given the the sum of the digits is even, that is $p+q+r$ is even, then

	Case	Number of ways
$\left(1\right)$	$p,q,r$ all even	$4\times 5\times 5=100$ ways
$\left(2\right)$	$p$ even and $q,r$ are odd	$4\times 5\times 5=100$ ways
$\left(3\right)$	$p$ odd and $q,r$ are even	$5\times 5\times 5=125$ ways
$\left(4\right)$	$q$ even and $p,r$ are odd	$5\times 5\times 5=125$ ways

Therefore, total number of ways$=100+100+125+125$

$=450$

Hence,$o\mathrm{ption}\left(\mathrm{A}\right)$ is the correct option.