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# A teacher prepares a test. She gives 5 objective type questi

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Intern
Joined: 23 Sep 2009
Posts: 1
A teacher prepares a test. She gives 5 objective type questi  [#permalink]

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11 Oct 2009, 01:24
11
00:00

Difficulty:

55% (hard)

Question Stats:

67% (02:06) correct 33% (02:34) wrong based on 151 sessions

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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
Manager
Joined: 11 Sep 2009
Posts: 129

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11 Oct 2009, 02:53
1
Two cases.

First Case: 2 Questions - 3 Choices, 2 Questions - 4 Choices

2C2 * 3C2 ways to select the questions
3C1 * 3C1 * 4C1 * 4C1 ways to answer the questions

= 1 * 3 * 3 * 3 * 4 * 4
= 27 * 16
= 432

Second Case: 1 Question - 3 Choices, 3 Questions - 4 Choices

2C1 * 3C3 ways to select the questions
3C1 * 4C1 * 4C1 * 4C1 ways to answer the questions

= 2 * 1 * 3 * 4 * 4 * 4
= 6 * 64
= 384

Total = 384 + 432
= 816
Manager
Joined: 18 Jul 2009
Posts: 166
Location: India
Schools: South Asian B-schools

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11 Oct 2009, 04:01
Good one 'AKProdigy87' i could solve upto
3 choices x 1 Q + 4 choices x 3 Q
3 choices x 2 Q + 4 choices x 2 Q

then i got all wrong...
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Bhushan S.
If you like my post....Consider it for Kudos

Math Expert
Joined: 02 Sep 2009
Posts: 47188

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17 Nov 2010, 11:11
1
3
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: $$432+384=816$$.

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Joined: 06 Sep 2013
Posts: 1866
Concentration: Finance
Re: A teacher prepares a test. She gives 5 objective type questi  [#permalink]

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29 Dec 2013, 18:13
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

Hope it helps
Cheers!

J
Manager
Joined: 21 Jul 2017
Posts: 139
Location: India
GMAT 1: 650 Q47 V33
GPA: 4
WE: Project Management (Education)
Re: A teacher prepares a test. She gives 5 objective type questi  [#permalink]

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01 Oct 2017, 05:05
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
Re: A teacher prepares a test. She gives 5 objective type questi &nbs [#permalink] 01 Oct 2017, 05:05
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