SOLUTION: An exam paper in mathematics contains 12 questions and students must answer 10 of them. a) in how many ways can a student choose 10 out of the 12 questions to answer? b) show, by

Question 892937: An exam paper in mathematics contains 12 questions and students must answer 10 of them.
a) in how many ways can a student choose 10 out of the 12 questions to answer?
b) show, by using the extended pigeonhole principle, that if 200 students write the exam paper, then at least 4 students will choose the same 10 questions to answer. state clearly what the pigeons and pigeonholes are.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
a) 12C10 = 12C2 = 12*11/2! = 66 ways
b) Assign each pigeon (student) to a pigeonhole (a subset of 10 questions to be answered). Since 200/66 > 3, there is a set of 10 questions that is answered by at least four students.
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