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A question paper consists of two sections A and B having respectively

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Bunuel
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A question paper consists of two sections A and B having respectively [#permalink] New post   11 Dec 2018, 02:39
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Question Stats:

47% (02:04) correct 53% (02:21) wrong based on 90 sessions
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A question paper consists of two sections A and B having respectively 3 and 4 questions. Four questions are to be solved to qualify in that paper. It is compulsory to solve at least one question from Section A and at least two questions from Section B. In how many ways can a candidate select the questions to qualify in that paper?


(A) 30
(B) 18
(C) 48
(D) 60
(E) 72

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A question paper consists of two sections A and B having respectively 3 and 4 questions. Four questions are to be solved to qualify in that paper. It is compulsory to solve at least one question from Section A and two questions from Section B. In how many ways can a candidate select the questions to qualify in that paper?
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A
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anshkool4u
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Re: A question paper consists of two sections A and B having respectively [#permalink] New post   11 Dec 2018, 02:50
Answer is 72,IMO.
Since 1 paper needs to be selected from set A,it can be done in 3 ways.
2 papers from set B can be selected in 4C2 ways,i.e 6 ways.
And the remaining 4 paper can be selected from the combined group of remaining 4 papers.
Hence,total no. Of ways,3*6*4= 72

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Re: A question paper consists of two sections A and B having respectively [#permalink] New post   12 Dec 2018, 00:45
only two cases would be there :

3c1*4c3 + 3c2*4c2 =
12+18 = 30

IMO A






[quote="Bunuel"]A question paper consists of two sections A and B having respectively 3 and 4 questions. Four questions are to be solved to qualify in that paper. It is compulsory to solve at least one question from Section A and at least two questions from Section B. In how many ways can a candidate select the questions to qualify in that paper?


(A) 30
(B) 18
(C) 48
(D) 60
(E) 72
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hibobotamuss
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Re: A question paper consists of two sections A and B having respectively [#permalink] New post   12 Dec 2018, 01:04
Why isn't the answer E? I am confused...
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abhishek893rai
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Re: A question paper consists of two sections A and B having respectively [#permalink] New post   12 Dec 2018, 01:15
(A) 30 as 3C1.4C3 + 3C2.4C2, rest all other combinations do not satisfy the minimum quantity requirement.

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daniformic
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Re: A question paper consists of two sections A and B having respectively [#permalink] New post   17 Nov 2020, 10:08
7!/3!4!=30

Ans A
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ism1994
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Re: A question paper consists of two sections A and B having respectively [#permalink] New post   21 Nov 2020, 04:18
daniformic wrote:
7!/3!4!=30

Ans A


you are wrong: 7!/3!4!=35
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Re: A question paper consists of two sections A and B having respectively [#permalink] New post   21 Nov 2020, 04:50
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Bunuel wrote:
A question paper consists of two sections A and B having respectively 3 and 4 questions. Four questions are to be solved to qualify in that paper. It is compulsory to solve at least one question from Section A and at least two questions from Section B. In how many ways can a candidate select the questions to qualify in that paper?


(A) 30
(B) 18
(C) 48
(D) 60
(E) 72



Case 1: 1 question correct in A, 3 questions correct in B
From the 3 questions in A, the number of ways to choose 1 to be correct = 3C1 = 3
From the 4 questions in B, the number of ways to choose 3 to be correct = 4C3 \(= \frac{4*3*2}{3*2*1} = 4\)
To combine these options, we multiply:
3*4 = 12

Case 2: 2 questions correct in A, 2 questions correct in B
From the 3 questions in A, the number of ways to choose 2 to be correct = 3C2 \(=\frac{3*2}{2*1} = 3\)
From the 4 questions in B, the number of ways to choose 2 to be correct = 4C2 \(= \frac{4*3}{2*1} = 6\)
To combine these options, we multiply:
3*6 = 18

Total number of ways = Case 1 + Case 2 = 12+18 = 30

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Re: A question paper consists of two sections A and B having respectively [#permalink] New post   02 Nov 2021, 07:27
3c2×4c2+ 3c1+4c3= 30

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Re: A question paper consists of two sections A and B having respectively [#permalink]
02 Nov 2021, 07:27
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