SOLUTION: A man has a total of n friends, he want to invite three of them for the dinner every day during the first 4 months of the year 2023. Calculate the minimum number of friends, n, he

Question 1194870: A man has a total of n friends, he want to invite three of them for the dinner every day during the first 4 months of the year 2023. Calculate the minimum number of friends, n, he must have if he does not want to invite the same combination of three friends more than once?
Answer by shlomitg(8) (Show Source): You can put this solution on YOUR website!
In the first 4 months of 2023 we have 120 days. We want to have at least 120 groups of 3 guests, so each group is invited only once.
The number of groups formed with 3 friends out of n, is n over 3 which equals:
n!/[3!(n-3)!]= n*(n-1)*n(-2)/6
we request that
n*(n-1)*n(-2)/6>=120
10*9*8=720 therefore n=10
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