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Sagot :
The smallest positive integer n so that you can avoid ever having the exact same group of three members over all 365 days is; 11
How to solve probability combination?
if we have n people and we want to do groups of 5, the total number of different combinations is:
ⁿC₅ = n!/((n - 5)!5!)
By using the Brute force method, we have;
If n = 5,
c = 5,
Thus;
C₅ = 5
If n = 6,
c = 6,
Thus;
C₅ = 6
If n = 7,
c = 7,
Thus
C₅ = 21
If n = 8,
c = 8,
Then;
C₅ = 56
Now, If n = 9,
C = 9!/((9 - 5)!5!)
C = 126
We want to find the smallest n such that c > 365. Thus, C = 126 is too small.
Let's try n = 11;
C = 11!/(6! * 5!) = 462
This is greater than 365 and so we need at least 11 members in the club.
Read more about Probability combination at; https://brainly.com/question/16830773
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