If the number of seven-digit numbers, such that the sum of their digits is even, is $m \cdot n \cdot 10^n ; m, n \in\{1,2,3, \ldots, 9\}$, then $m+n$ is equal to__________
Answer (integer)
14
Solution
<p>When numbers are uniformly distributed, half of them have even digit sums and half have odd digits sums.</p>
<p>Number of 7-digit numbers with even digit sum =</p>
<p>$\frac{1}{2} \cdot 9 \cdot 10^6=4.5 \cdot 10^6$</p>
<p>Note that $9 \cdot 5 \cdot 10^5=4.5 \cdot 10^6$</p>
<p>$m+n=9+5=14$</p>
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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