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# Counting

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105
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Help I have spent a long time on this

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 100 days?

Jan 28, 2023

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You should have specified that of the "n" people, how many of them do you intend to use to review a book!

1 - If you intend to use 2 people, then minimum n = 15. Because 15 C 2 =105 unique combinations

2 - ................................3.......................................n = 10. .............. 10 C 3 = 120 ................................

3 - ................................ 4 .................................... n  = 9 ................. 9 C 4 = 126 .................................

4 - ................................ 5 .................................... n  = 9 .................. 9 C 5 = 126 .................................

5 - ...............................  6 ...................................  n  = 10 ................ 10 C 6 = 210 ...............................

And so on...............!

Jan 28, 2023