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Permutation / Combinations

by serenayc » Thu May 03, 2012 8:02 pm
Hi, would someone please explain how the derive the answer for the following problem:

In how many ways can a teacher write an answer key for a mini-quiz that contains 3 T/F questions followed by 2 multiple-choice questions with 4 answer choices each, if the correct answer to all T/F questions cannot be the same?

[Answer]: 96
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by Shalabh's Quants » Thu May 03, 2012 10:15 pm
serenayc wrote:Hi, would someone please explain how the derive the answer for the following problem:

In how many ways can a teacher write an answer key for a mini-quiz that contains 3 T/F questions followed by 2 multiple-choice questions with 4 answer choices each, if the correct answer to all T/F questions cannot be the same?

[Answer]: 96
The no. of ways to answer 3 T/F questions = 2*2*2 = 8.

The no. of ways to answer 3 T/F questions with NO T/T/T or F/F/F answer pattern(Not permitted) = 2.

So Permitted ways to answer 3 T/F questions = 8 - 2 =6.

The no. of ways to answer 2 multiple-choice questions with 4 answer choices = 4*4 = 16.

The no. of ways to answer 3 T/F questions & 2 multiple-choice questions with 4 answer choices if the correct answer to all T/F questions cannot be the same = 16*6 = 96.
Shalabh Jain,
e-GMAT Instructor
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