Permutation and Combination

[sukhman]

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

[vinay1983]

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!

[vishnum]

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.



Br,
Vishnu.

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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