JEE MAIN - Mathematics (2020 - 4th September Evening Slot - No. 1)
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
135
Explanation
Select any 4 questions in 6C4
ways which are
correct.
Answering right option for each question is possible in 1 way.
So ways of choosing right option for 4 questions = 1.1.1.1 = (1)4
Number of ways of choosing wrong option for each question = 3
So ways of choosing wrong option for 2 questions = (3)2
$$ \therefore $$ Required number of ways = 6C4.(1)4.(3)2 = 135
Answering right option for each question is possible in 1 way.
So ways of choosing right option for 4 questions = 1.1.1.1 = (1)4
Number of ways of choosing wrong option for each question = 3
So ways of choosing wrong option for 2 questions = (3)2
$$ \therefore $$ Required number of ways = 6C4.(1)4.(3)2 = 135
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