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Permutation and Combination

by sukhman » Tue Sep 10, 2013 5:34 am
In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions
followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same? Answer - 2 × 2 × 2 × 4 × 4 - 2 × 1 × 1 × 4 × 4 = 96
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by vinay1983 » Tue Sep 10, 2013 8:44 am
sukhman wrote:In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions
followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?

Answer - [spoiler]2 × 2 × 2 × 4 × 4 - 2 × 1 × 1 × 4 × 4 = 96[/spoiler]

Please use spoiler or try to know the correct procedure to post such posts!

No offence!
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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by vishnum » Thu Sep 12, 2013 5:20 am
Hi,

My approach is as below:

T-F questions- 2 ways for each question. so 3 questions will be done in 2^3 ways. But we need to drop same answer for all 3 questions (i.e., TTT & FFF). So it is 2^3-2 = 4

Multiple choice question - 4 ways for each question - 4^2 for 2 questions = 16

As both events are independent 16*4 = 64.



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Vishnu.
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by [email protected] » Thu Sep 12, 2013 11:58 am
Hi vishnum,

Your logic is correct, BUT you made a silly math mistake:

2^3 = 8

8 - 2 = 6 ..... NOT 4

So the final answer is [spoiler]6(4)(4) =96[/spoiler]

For what it's worth, it's these types of silly math mistakes that KILL Test Takers.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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