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Combination: No. of possible answers

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Combination: No. of possible answers

by Naruto » Sun Jun 14, 2009 4:17 am
A teacher prepares a test. She gives 5 objective type questions out of which four have to be answered. Find out total no. of ways in which it can be answered if the first two questions have 3 answer choices and the last two questions have 4 choices.

A. 222
B. 816
C. 192
D. 100
E. 144



Well according to my calculation the answer was 832. Now thats not an option here. Please give the solution. Will post OA later.
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by tohellandback » Sun Jun 14, 2009 6:21 am
you sure you typed the question correct. Plz check ..I think information about 3rd question is required
The powers of two are bloody impolite!!
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by Naruto » Sun Jun 14, 2009 7:53 am
tohellandback wrote:you sure you typed the question correct. Plz check ..I think information about 3rd question is required
Right my mistake it says the last three questions instead of last two.
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by tohellandback » Sun Jun 14, 2009 8:27 am
IMO B,

IMO E. 144
two questions with 3 answer choices and 3 questions with 4 answer choices
we have two combinations available
1 three answer choice question and 3 four answer choice question

or,

2 three answer choice questions and 2 four answer choice question

for case1)

1 question can be selected in 2 ways from the three answer choice questions
so total number of ways to answer=2*3=6

3 four answer choice question can be selected in 1 way.
total number of ways these questions can be answered is 4*4*4=64
total number of ways the 4 questions can be answered=6*64=384

case 2:
2 question can be selected in 1 way from the three answer choice questions
these two questions can be answered in 3*3=9 ways
2 question can be selected in 3 way from the four answer choice questions
these questions can be answered in 4*4*3 ways=48
total number of ways this set of questions can be answered=9*48=432

total number of ways=432+384=816
The powers of two are bloody impolite!!
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