Help I need to use combinations

I run a book club with n people, not including myself. Every day, for 100 days, I invite 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 members over all 365 days?

Guest Apr 13, 2023

#1**0 **

if we have n people and we want to do groups of 5, the total number of different combinations is:

find the smallest n such c > 365.

let's do it by brute force:

if n = 5, we have:

if n = 6

if n = 7

if n = 8

if n = 9

so 9 is not enough, let's see N = 10

C = 10!/(5!*5!) = 252

10 is not enough, let's see with 11.

C = 11!/(6!*5!) = 462

So you need at least 11 members in the club.

Then the minimum number of members such we have more than 365 combinations is 11 members

RyanTaylor Apr 13, 2023