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Can someone explain me the solution?
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02 Jan 2018, 11:21
02 Jan 2018, 11:21
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75% (02:23) correct
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A teacher prepares a test. She gives 5 objective type questions out of which 4 have to be answered. Find the total ways in which they can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices.
A. 255
B. 816
C. 192
D. 100
E. 144
A. 255
B. 816
C. 192
D. 100
E. 144
Re: Can someone explain me the solution?
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02 Jan 2018, 12:30
02 Jan 2018, 12:30
1
Expert Reply
Please specify the official answer.
Now there are 5 questions and we have to select 4. Now there are two ways of doing this.
Case 1. Select first two questions and last two from remaining 3.
Case 2. Select one question from first 2 and last 3.
Case 1: Number of ways of selecting = \(C_2^3\) = 3 Namely {1 2 3 4}{1 2 3 5}{1 2 4 5}
Case 2: Number of ways of selecting = \(C_1^2\) = 2 Namely {1 3 4 5}{2 3 4 5}
Now in Case 1 first two questions have 3 choices and last two questions have 4 choices. Hence total choices possible for case 1 = 3 * 3 * 4* 4 = 144.
Case 2 fist question has 3 choices and remaining has 4 choices Hence total choices possible for case 1 = 3 * 4 * 4* 4 = 192
Combining both we have = 144*3 + 192*2 = 816.
Hence option B.
PLEASE SHARE THE OFFICIAL ANSWER AS WELL AS THE SOURCE OF THE QUE.
PS: I don't think this is a GRE QUE
Now there are 5 questions and we have to select 4. Now there are two ways of doing this.
Case 1. Select first two questions and last two from remaining 3.
Case 2. Select one question from first 2 and last 3.
Case 1: Number of ways of selecting = \(C_2^3\) = 3 Namely {1 2 3 4}{1 2 3 5}{1 2 4 5}
Case 2: Number of ways of selecting = \(C_1^2\) = 2 Namely {1 3 4 5}{2 3 4 5}
Now in Case 1 first two questions have 3 choices and last two questions have 4 choices. Hence total choices possible for case 1 = 3 * 3 * 4* 4 = 144.
Case 2 fist question has 3 choices and remaining has 4 choices Hence total choices possible for case 1 = 3 * 4 * 4* 4 = 192
Combining both we have = 144*3 + 192*2 = 816.
Hence option B.
PLEASE SHARE THE OFFICIAL ANSWER AS WELL AS THE SOURCE OF THE QUE.
PS: I don't think this is a GRE QUE
General Discussion
Re: Can someone explain me the solution?
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04 Jun 2024, 08:27
04 Jun 2024, 08:27
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
