Math Problem Statement

uppose that 25 people sit around a huge circular table. How many ways are there to select 4 of these people, such that any 2 selected people have at least two people between them?

Solution

We are tasked with determining how many ways there are to select 4 people from a group of 25 seated around a circular table such that any two selected people have at least two people between them.

Step 1: Simplifying the Problem

To make the problem easier, consider the seating as a linear arrangement instead of a circular one. First, let's label the 25 people from P1P_1 to ( P_{

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Circular Permutations
Constraints in Selection

Formulas

Combination formula: C(n, k) = n! / (k! * (n - k)!)

Theorems

Circular permutation theorem
Stars and bars method (for constraints)

Suitable Grade Level

Grades 10-12