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In a Question paper there are 4 multiple choice questions

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In a Question paper there are 4 multiple choice questions  [#permalink]

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New post Updated on: 18 Oct 2012, 13:57
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Question Stats:

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In a Question paper there are 4 multiple choice questions. Each question has 5 choices with only one choice as the correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?

A. 19
B. 85
C. 120
D. 624
E. 1024

Originally posted by avaneeshvyas on 18 Oct 2012, 13:54.
Last edited by Bunuel on 18 Oct 2012, 13:57, edited 1 time in total.
Renamed the topic.
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Re: In a Question paper there are 4 multiple choice questions  [#permalink]

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New post 18 Oct 2012, 14:03
4
4
avaneeshvyas wrote:
In a Question paper there are 4 multiple choice questions. Each question has 5 choices with only one choice as the correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?

A. 19
B. 85
C. 120
D. 624
E. 1024


A candidate can answer the test in 5*5*5*5=5^4 number of ways (each question has 5 choices and we have total of 4 questions). Now, out of these cases there will be only one case when the candidate answered all the four questions correct. Therefore the total number of ways in which a candidate will NOT get all the four answers correct is 5^4-1=624.

Answer: D.

Hope it's clear.
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Re: PnC Problem :In a Question paper there are 4 multiple choice  [#permalink]

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New post 18 Oct 2012, 13:56
I tried this solving by the following method:
since there are 4 ways of getting the question wrong, hence the total no. of combinations required would be
4*4*4*4*4(5 times) = 1024..... which is wrong...so please explain the flaw in my understanding
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Re: In a Question paper there are 4 multiple choice questions  [#permalink]

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New post 18 Oct 2012, 14:15
Bunuel wrote:
avaneeshvyas wrote:
In a Question paper there are 4 multiple choice questions. Each question has 5 choices with only one choice as the correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?

A. 19
B. 85
C. 120
D. 624
E. 1024


A candidate can answer the test in 5*5*5*5=5^4 number of ways (each question has 5 choices and we have total of 4 questions). Now, out of these cases there will be only one case when the candidate answered all the four questions correct. Therefore the total number of ways in which a candidate will NOT get all the four answers correct is 5^4-1=624.

Answer: D.

Hope it's clear.



Very stupid indeed on my part...need to sleep i guess...... :oops: :oops: :oops: :oops:
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Re: In a Question paper there are 4 multiple choice questions  [#permalink]

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New post 25 Sep 2015, 06:22
Bunuel wrote:
avaneeshvyas wrote:
In a Question paper there are 4 multiple choice questions. Each question has 5 choices with only one choice as the correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?

A. 19
B. 85
C. 120
D. 624
E. 1024


A candidate can answer the test in 5*5*5*5=5^4 number of ways (each question has 5 choices and we have total of 4 questions). Now, out of these cases there will be only one case when the candidate answered all the four questions correct. Therefore the total number of ways in which a candidate will NOT get all the four answers correct is 5^4-1=624.

Answer: D.

Hope it's clear.


Bunuel,

I could not understand how did you calculate that there will be only one case when the candidate answered all the four questions correct.
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Re: In a Question paper there are 4 multiple choice questions  [#permalink]

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New post 25 Sep 2015, 08:17
1
Learning4mU wrote:
Bunuel wrote:
avaneeshvyas wrote:
In a Question paper there are 4 multiple choice questions. Each question has 5 choices with only one choice as the correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?

A. 19
B. 85
C. 120
D. 624
E. 1024


A candidate can answer the test in 5*5*5*5=5^4 number of ways (each question has 5 choices and we have total of 4 questions). Now, out of these cases there will be only one case when the candidate answered all the four questions correct. Therefore the total number of ways in which a candidate will NOT get all the four answers correct is 5^4-1=624.

Answer: D.

Hope it's clear.


Bunuel,

I could not understand how did you calculate that there will be only one case when the candidate answered all the four questions correct.


There is only one correct answer to each question. So, there is 1*1*1*1=1 way to answer all 4 questions correctly.
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Re: In a Question paper there are 4 multiple choice questions  [#permalink]

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New post 11 Nov 2017, 00:20
IMO:

4 questions with each having 5 options.
There are total 5 ^4 patterns in which a student can respond.

Hence total ways of responding-5^4= 625
Now, there is 1 way which contains all 4 answers incorrect by a student.

Hence we need to subtract that-
Hence Answer = 5^4 -1= 625-1 = 624

IMO option D is answer
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Re: In a Question paper there are 4 multiple choice questions  [#permalink]

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New post 14 Nov 2017, 07:04
avaneeshvyas wrote:
In a Question paper there are 4 multiple choice questions. Each question has 5 choices with only one choice as the correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?

A. 19
B. 85
C. 120
D. 624
E. 1024


We can use the following equation:

Total number of ways to answer all questions - number of ways to get all questions correct = the total number of ways in which a candidate will not get all four answers correct

5 x 5 x 5 x 5 - 1 x 1 x 1 x 1 = 625 - 1 = 624

Answer: D
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Re: In a Question paper there are 4 multiple choice questions  [#permalink]

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New post 30 Dec 2018, 09:55
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Re: In a Question paper there are 4 multiple choice questions   [#permalink] 30 Dec 2018, 09:55
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