Permutations & Combinations: Non-consecutive selection on a circle Formula proof with examples

Permutations & Combinations: Non-consecutive selection in a row
Formula proof: Number of ways of selecting r objects from n arranged objects on a circle so that no two objects are consecutive is n/r.n-r-1Cr-1

Example 1: Find the number of ways of selecting 4 objects from n arranged objects on a circle so that no two objects are consecutive ?
Example 2: Find the number of triangles that can be formed from vertices of an octagon such that they do not have a common side with the octagon?

Link to non-consecutive selection in a row video:    • Permutations & Combinations: Non-cons...  
Link to circular permutation video:    • Concept Check | Linear vs Circular pe...  
Link to consecutive selection video:    • Permutations & Combinations: Consecut...  

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