+0  
 
+1
39
6
avatar+24 

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

 Apr 13, 2022
 #1
avatar+326 
+2

Can you please write who many days... I don't think the latex is showing....

 Apr 13, 2022
 #2
avatar+326 
+2

A question similar to this has been answered:

 

https://web2.0calc.com/questions/help-please_8381

 

If you can write the latex, or tell me what numbers are in the problem, I can help you if needed.

 

smiley

 Apr 13, 2022
 #3
avatar
+1

oh sorry D:

I run a book club with n people, not including myself. Every day, for 365  days, I invite three 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 three members over all   365 days?
 

Guest Apr 13, 2022
 #4
avatar+1351 
+2

You need \({n \choose 3} \ge 365\)

 

The smallest number that satisfies this is \(\color{brown}\boxed{15}\)

BuilderBoi  Apr 13, 2022
 #5
avatar
+1

14 C 3 = 364

 

15 c 3 = 455

Guest Apr 13, 2022
 #6
avatar+24 
+1

thanks, both of you!! laugh

 Apr 13, 2022

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