Question

The total number of $3$-digit numbers, the sum of whose digits is even, is equal to

• A. 450
• B. 350
• C. 250
• D. 325

Answer 1

Answer: (A)

Let the number be $n=pqr$.
As $p+q+r$ is even,
there are following cases:
(i) $p,q,r$ all are even $\to 4\cdot 5\cdot 5$
$=100$ ways
(ii) $p$ even and $q,r$ are odd $\to 4\cdot 5\cdot 5$
$=100$ ways
(iii) $p$ odd, $q$ and $r$ even $\to 5\cdot 5\cdot 5$
$=125$ ways
(iv) $p$ odd, $q$ even, $r$ odd $\to 5\cdot 5\cdot 5=125$
Total ways $=100+100+125+125=450$