4. Qana,Qina and Quna are three lecturer that teaching Calculus subject during t

Question

4. Qana,Qina and Quna are three lecturer that teaching Calculus subject during the short semester break. They decided to make a different set of assignment question to each student. Every set of question must consist of 5 question since Calculus subject has 4 chapters.With the knowledge of discrete mathematics,Kindly find and list all the consequence different set of assignment question if all of them only make 4 question each. And find how many maximum numbers of students can be in the short semester if each student gets different set of question.

Explanation / Answer

Let no. of students be = n .

Assuming there must be at least 1 question from each chapter .

Together they contribute 4 questions each . so total no. of questions = 3X4 = 12 .

Assuming all 12 questions are different ,

Each of consequent set contains 4 questions only . so there are n sets each having 4 questions .

No 2 sets are same but taken any 2 of them , they may have some questions ( 1,2 or 3 ) in common .

So starting from the bottom , n sets not completely disjoint are there .

Assume the n sets are completely disjoint . Then the problem can be modelled as partition of questions where 4 chapters can be treated as partitions on the calculus taught .

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