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

Thanks in advance for anyone who helps ^0^

Guest Feb 28, 2020

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$\text{What you need is $n \ni \dbinom{n}{4} \geq 365$}\\ \text{Whipping out our pocket Pascal's Triangle we see that}\\ \dbinom{11}{4} = 330\\ \dbinom{12}{4} = 495\\ \text{So a group of 12 people and you're good to go}$

Rom Feb 28, 2020

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"Pocket Pascal's Triangle " ⇒ LOL!!!!

CPhill Feb 28, 2020

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Thank you ^0^

I haven't learned about Pascal's Triangles yet, so I'll go and search them up and see if I can do my other homeworks by myself.

Guest Feb 28, 2020

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Rom · Answer 1 · 2020-02-28T04:06:14

$\text{What you need is $n \ni \dbinom{n}{4} \geq 365$}\\ \text{Whipping out our pocket Pascal's Triangle we see that}\\ \dbinom{11}{4} = 330\\ \dbinom{12}{4} = 495\\ \text{So a group of 12 people and you're good to go}$

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