Hi, I'm trying so solve following problem:
Let's say, we have a set A={1,2,3,.....49}.
Now, I am defining sets A1, A2, A3,....An as follow: A1={a1,a2,a3,....a30}, A2={b1,b2,b3,...b30}, and so on, where all elements of sets Ai are also elements of set A, which means they are subsets of set A. (All sets Ai have 30 elements).
Now, I am looking for a set C={ {A1},{A2},{A3},....{An} } so, that if I pick randomly 6 elements of set A, they will be (at least) in one of sets Ai.
What is n? Let's see: first of all, how much possibilities are to pick 6 elements of set A? There are (49*48*47*46*45*44)/6!=13.983.816
Secondly, how much of these posibilities covers one of sets Ai? Because set Ai has 30 elements, it covers (30*29*28*27*26*25)/6!=593.775
Now dividing both results, it gives 23,55 what means, that we need at least n=24 (probably more, I don't sure).
So the question is, how to find this set C?
Let's say, we can start so: A1={1,2,3,....30}, this will be first set. But what next? With some algorithm I can implement it in C or Java, but I dont know how to start. Thanks.
Let's say, we have a set A={1,2,3,.....49}.
Now, I am defining sets A1, A2, A3,....An as follow: A1={a1,a2,a3,....a30}, A2={b1,b2,b3,...b30}, and so on, where all elements of sets Ai are also elements of set A, which means they are subsets of set A. (All sets Ai have 30 elements).
Now, I am looking for a set C={ {A1},{A2},{A3},....{An} } so, that if I pick randomly 6 elements of set A, they will be (at least) in one of sets Ai.
What is n? Let's see: first of all, how much possibilities are to pick 6 elements of set A? There are (49*48*47*46*45*44)/6!=13.983.816
Secondly, how much of these posibilities covers one of sets Ai? Because set Ai has 30 elements, it covers (30*29*28*27*26*25)/6!=593.775
Now dividing both results, it gives 23,55 what means, that we need at least n=24 (probably more, I don't sure).
So the question is, how to find this set C?
Let's say, we can start so: A1={1,2,3,....30}, this will be first set. But what next? With some algorithm I can implement it in C or Java, but I dont know how to start. Thanks.