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avatar+1791 

I run a book club with $n$ people, not including myself.  Every day, for $100$ days, I invite $14$ members in the club to review a book.  What is the smallest positive integer $n$ so that I can avoid ever having the exact same group of $14$ members over all $100$ days?

 Jan 12, 2024
 #1
avatar+128732 
+1

C (n , 14) =  100

 

   n!

____________      =  100  different sets

(n -14)! * 14!

 

n! / (n -14)!  =  100 * 14!   

 

Solving this by hand is difficult

 

WolframAlpha  shows  n  to be ≈ 15.9

 

C (15 , 14)  = 15  different  sets

 

C (16, 14)  = 120  different sets

 

So  n  = 15 days

 

cool cool cool

 Jan 12, 2024

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