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?
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