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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?

 Apr 9, 2024
 #1
avatar+128794 
+1

We need to solve this

 

C (n ,14)  >  100

 

By brute force

 

C (15,14)  =  15

 

C ( 16 ,14)    =  120

 

So......n =  16

 

cool cool cool

 Apr 9, 2024

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