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Re: Combinatronics [#permalink]
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azule45 wrote:
A teacher prepares a test. she gives 5 objective type questions out of which 4 must be answered. find the total ways in which they can be answered if the first two questions have 3 choices, and the last 3 questions have 4 choices.

A. 255
B. 816
C. 192
D. 100
E. 144


So there are two types of questions: two with 3 choices and three with 4 choices.

In order to answer exactly 4 out of 5 then either both from the first type and any two from the second type must be answered OR any from the first type and all three from the second type.

First case: \((3*3)*(C^2_3*4*4)=432\);
Second case \((C^1_2*3)*(4*4*4)=384\);

So total: \(432+384=816\).

Answer: B.
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Re: A teacher prepares a test. She gives 5 objective type questi [#permalink]
jaymodi123 wrote:
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


So we have 5 questions, pick 4

Only two ways to pick them are:

1 of the three choice questions and 3 of the 4 choice questions OR 2 of each

First scenario (2C1)(3)(4^3) = 384

Second scenario (3C2)(3^2)(4^2) = 432

Add both = 816, or you know what don't even add them just note that UD has to be 6 only 1 answer choice that is b

Hence answer is (B)

Hope it helps
Cheers!

J :)
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Re: A teacher prepares a test. She gives 5 objective type questi [#permalink]
First Case: 2 Questions with 3 Choices; 2 Questions with 4 Choices

2C2 * 3C2 ways to select the questions
and ways to answer = 3C1 * 3C1 * 4C1 * 4C1
= 1 * 3 * 3 * 3 * 4 * 4
= 27 * 16
= 432

Second Case: 1 Question with 3 Choices; 3 Questions with 4 Choices
2C1 * 3C3 ways to select the questions and 3C1 * 4C1 * 4C1 * 4C1 ways to answer the questions
= 2 * 1 * 3 * 4 * 4 * 4
= 6 * 64
= 384

Total = 384 + 432
= 816
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Re: A teacher prepares a test. She gives 5 objective type questi [#permalink]
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Re: A teacher prepares a test. She gives 5 objective type questi [#permalink]
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