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Can someone explain me the solution?

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Intern
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Can someone explain me the solution? [#permalink] New post 02 Jan 2018, 11:21
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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
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GMAT Club Legend
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Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Re: Can someone explain me the solution? [#permalink] New post 02 Jan 2018, 12:30
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Expert's post
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
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Sandy
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Re: Can someone explain me the solution?   [#permalink] 02 Jan 2018, 12:30
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