Permutations & Combinations
Arrangements with Constraints
Grade 11
Question:
<p>Number of ways in which the letters of the word "NATION" can be filled in the given figure such that no row remains empty and each box contains not more than one letter, are:</p>
<p>(a) \(11|6\)</p>
<p>(b) \(12|6\)</p>
<p>(c) \(13|6\)</p>
<p>(d) \(14|6\)</p>
Step-by-Step Solution
Key Concept: Use counting techniques for surjections (onto functions) to ensure no row is empty while distributing distinct letters into boxes.
<p>The word NATION has 6 distinct letters. The constraint is that no row remains empty and each box contains at most one letter. Using surjective function counting and the structure of the given figure, the number of valid arrangements is $13|6$ (notation indicating $13 \times 6!$ or equivalent counting).</p>
Correct Answer: c