Permutations & Combinations
Grade None
Question:
<p>Let A<sub>1</sub>, A<sub>2</sub>, A<sub>3</sub> ,............. A<sub>n</sub> are the vertices of a polygon of sides n. If the pentagons that can be constructed by joining these vertices such that none of the side of the polygon is also the side of the pentagon is 36, then the value of n is equal to:</p>
<p style="display:inline">10</p>
<p style="display:inline">11</p>
<p style="display:inline">12</p>
<p style="display:inline">8</p>
Step-by-Step Solution
Key Concept: The number of ways to select k non-adjacent vertices from a polygon with n vertices is determined by the circular selection formula n/(n-k) * C(n-k, k).
<p>12</p>
Correct Answer: C