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# In a Question paper there are 4 multiple choice questions

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Intern
Joined: 11 Jul 2012
Posts: 47
GMAT 1: 650 Q49 V29
In a Question paper there are 4 multiple choice questions  [#permalink]

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Updated on: 18 Oct 2012, 13:57
17
00:00

Difficulty:

35% (medium)

Question Stats:

69% (01:50) correct 31% (02:11) wrong based on 240 sessions

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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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Posts: 60627
Re: In a Question paper there are 4 multiple choice questions  [#permalink]

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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.

Hope it's clear.
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Intern
Joined: 11 Jul 2012
Posts: 47
GMAT 1: 650 Q49 V29
Re: PnC Problem :In a Question paper there are 4 multiple choice  [#permalink]

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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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Joined: 11 Jul 2012
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GMAT 1: 650 Q49 V29
Re: In a Question paper there are 4 multiple choice questions  [#permalink]

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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.

Hope it's clear.

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

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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.

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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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.

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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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

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

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14 Nov 2017, 07:04
1
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

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

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23 Nov 2019, 08:28
1
Top Contributor
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

Let's first determine the TOTAL number of ways the test can be completed.
The 1st question can be answered in 5 different ways (A, B, C, D, or E).
The 2nd question can be answered in 5 different ways (A, B, C, D, or E).
The 3rd question can be answered in 5 different ways (A, B, C, D, or E).
The 4th question can be answered in 5 different ways (A, B, C, D, or E).

By the Fundamental Counting Principle (FCP), the total number of ways we can complete test = (5)(5)(5)(5) = 625 ways

So, there 625 possible outcomes
Among those 625 possible outcomes, ONLY 1 outcome is such that all four questions ARE answered correctly.
This means, in the remaining 624 outcomes, the four questions are NOT all answered correctly.

Cheers,
Brent
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Re: In a Question paper there are 4 multiple choice questions  [#permalink]

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23 Nov 2019, 12:36
Is there another, albeit less elegant, way to solve this problem?

You cannot answer all 4 questions correctly, so I was trying to add the combinations of 3 correct, 2 correct, 1 correct and none correct and adding them together.

For example, for 3 correct, you have 3*(5C1) (3 correct answers) * 1*(5C4) (for the incorrect answer).

Can't seem to get the correct answer using this method though. Thoughts?
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Posts: 4
Re: In a Question paper there are 4 multiple choice questions  [#permalink]

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26 Nov 2019, 14:08
I got this question wrong because I attempted to use factorials (i.e., 5! * 4!).

Can someone please explain when it is appropriate to use factorials, and when we should simply multiply the number of options together repeatedly (like in this question)?

Thanks!
Re: In a Question paper there are 4 multiple choice questions   [#permalink] 26 Nov 2019, 14:08
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