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Fritz is taking an examination that consists of two parts, A

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Fritz is taking an examination that consists of two parts, A [#permalink] New post 09 May 2019, 01:16
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Fritz is taking an examination that consists of two parts, A and B, with the following instructions:

Part A contains three questions, and a student must answer two.
Part B contains four questions, and a student must answer two.
Part A must be completed before starting Part B.

In how many ways can the test be completed?

(A) 12

(B) 15

(C) 36

(D) 72

(E) 90
[Reveal] Spoiler: OA

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Re: Fritz is taking an examination that consists of two parts, A [#permalink] New post 10 May 2019, 06:04
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This can be done by using the fundamental principle of counting.

There are altogether 5 slots for solving the problem.

In the first slot we have 1 because we have to attempt part A first.
In the second slot we have 3 because there are 3 options for first part.
After one of the option is chosen the third slot will contain 2 option.
After first part is complete there remains two slot.
These two slots will contain number 4 and 3 respectively because for second part there are 4 options and two must be done.
Therefore ans = 1*3*2*4*3 = 72
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Re: Fritz is taking an examination that consists of two parts, A [#permalink] New post 28 Aug 2019, 01:55
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Carcass wrote:
Fritz is taking an examination that consists of two parts, A and B, with the following instructions:

Part A contains three questions, and a student must answer two.
Part B contains four questions, and a student must answer two.
Part A must be completed before starting Part B.

In how many ways can the test be completed?

(A) 12

(B) 15

(C) 36

(D) 72

(E) 90


I think that the question is a bit unclear as it doesn't specify if the order of the questions within each part matters.
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Re: Fritz is taking an examination that consists of two parts, A [#permalink] New post 28 Aug 2019, 14:33
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In this case no need to specify.

The order inside the tests does not matter..

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Re: Fritz is taking an examination that consists of two parts, A [#permalink] New post 03 Sep 2019, 11:41
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The question is unclear and the answer is incorrect. First of all, it is not stated whether the student has to answer exactly or at least two (or three) questions. If a student answered exactly three questions it is true that he answered 2 questions (it is whilst not true that he answered exactly two questions). Moreover, if the order inside each part does not matter (as the author of the question claimed above), then in case of exactly 2 and exactly 3 questions the answer should be Binomial(3, 2)*Binomial(4, 2) = 3*6 = 18. So, 72 is a correct answer only if we assume that firstly student has to answer exactly 2 questions in part A and exactly 3 questions in part B and additionally order of answers matters (i.e. to answer the 1st question and then answer the 2nd is different from answer the 2nd and then answer the 1st).
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Re: Fritz is taking an examination that consists of two parts, A [#permalink] New post 03 Sep 2019, 11:46
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fltft wrote:
The question is unclear and the answer is incorrect. First of all, it is not stated whether the student has to answer exactly or at least two (or three) questions. If a student answered exactly three questions it is true that he answered 2 questions (it is whilst not true that he answered exactly two questions). Moreover, if the order inside each part does not matter (as the author of the question claimed above), then in case of exactly 2 and exactly 3 questions the answer should be Binomial(3, 2)*Binomial(4, 2) = 3*6 = 18. So, 72 is a correct answer only if we assume that firstly student has to answer exactly 2 questions in part A and exactly 3 questions in part B and additionally order of answers matters (i.e. to answer the 1st question and then answer the 2nd is different from answer the 2nd and then answer the 1st).


Agreed! Way too much ambiguity!!
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Re: Fritz is taking an examination that consists of two parts, A [#permalink] New post 03 Sep 2019, 12:04
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Added to the list of not a good question we are looking for :)
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Re: Fritz is taking an examination that consists of two parts, A   [#permalink] 03 Sep 2019, 12:04
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Fritz is taking an examination that consists of two parts, A

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