Question

Use the pigeonhole principle to prove the following statement: Suppose teacher gives a Two questions multiple-choice quiz Such that each question has three options (A,B, C) for students to chose the correct answer. If she has 10 student then at least two will turn in identical quizzes.

Answer 1

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here we have 2 question ,, each question have 3 options ..

so , all cases which students take are { AA , AB , AC , BA , BB , BC , CA , CB , CC }  

so these are total 9 cases ..

by using pigeon hole principal , if we have 10 students then if 9 students take different options then 10th student pick options which is same as any of previous 9 ..

so , atleast two will turn identically quizzes ..