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There are 15 questions in a test paper in which the question

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There are 15 questions in a test paper in which the question [#permalink] New post 11 Nov 2012, 10:26
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There are 15 questions in a test paper in which the questions need to be correctly matched with 15 answer choices. A student is awarded 6 marks for a correct answer. What is the maximum number of students who give different sets of correct answers and get 66 marks in the test

a. 13600
b. 12285
c. 14480
d. 13845
e. None of these
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Re: There are 15 questions in a test paper in which the question [#permalink] New post 11 Nov 2012, 22:38
The number of ways to choose 11 questions to be answered correctly from the 15 = 15C11 = 1365
The number of ways of answering the 4 remaining questions wrongly = 4![1/2! - 1/3! + 1/4!] = 9 (derangement formula)

Therefore the maximum number of students = 1365 * 9 = 12285

Option (B)
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Manager
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Re: There are 15 questions in a test paper in which the question [#permalink] New post 11 Nov 2012, 23:27
GyanOne wrote:
The number of ways to choose 11 questions to be answered correctly from the 15 = 15C11 = 1365
The number of ways of answering the 4 remaining questions wrongly = 4![1/2! - 1/3! + 1/4!] = 9 (derangement formula)

Therefore the maximum number of students = 1365 * 9 = 12285

Option (B)



Hi Gyanone can you please explain this part?? " 4![1/2! - 1/3! + 1/4!]"
Re: There are 15 questions in a test paper in which the question   [#permalink] 11 Nov 2012, 23:27
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