Permutations & Combinations
Geometric Selections
Grade 11
Question:
<p>Number of quadrilaterals of which exactly two adjacent sides of the quadrilateral are common to the sides of the n-gon, where \(n = 10\).</p>
Step-by-Step Solution
Key Concept: Count quadrilaterals with exactly two adjacent sides common to an n-gon sides using combinatorial selection.
<p><strong>Solution:</strong></p><p>The number of such quadrilaterals is given by $n \times \binom{n-5}{1} = n(n-5)$</p><p>With $n = 10$: $10 \times 5 = 50$</p>
Correct Answer: 50