A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is __________.
Answer (integer)
135
Solution
Select any 4 questions in <sup>6</sup>C<sub>4</sub>
ways which are
correct.
<br><br>Answering right option for each question is possible in 1 way.
<br><br>So ways of choosing right option for 4 questions = 1.1.1.1 = (1)<sup>4</sup>
<br><br>Number of ways of choosing wrong option for each question = 3
<br><br>So ways of choosing wrong option for 2 questions = (3)<sup>2</sup>
<br><br>$\therefore$ Required number of ways = <sup>6</sup>C<sub>4</sub>.(1)<sup>4</sup>.(3)<sup>2</sup> = 135
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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