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saby1410
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In how many ways can a teacher write an answer key for a min 22 Jul 2021, 12:40
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Bunuel
pacifist85
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?

A. 88
B. 90
C. 96
D. 98
E. 102


Hello, I ended up in the same answer, but I think that I read the question in a totally different way... Your opinion on this would be very useful!

I used this way (trying to arrange the questions in an answer sheet):
We have 3 TF questions and 2 MC questions, which have 4 answer choices each.

The TF questions could be arranged in 3 different ways. Each one of them 1st, 2nd or 3rd
Each MC question could be arranged in 4*4= 16 ways. So, the 2 MC questions in 16*2= 32 ways.

So, 3*32= 96

Ws

Was this just a lucky mistake?

Thank you.

This is wrong. We have 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each:

Q1: ?
Answer: True or False

Q2: ?
Answer: True or False

Q3: ?
Answer: True or False


M1: ?
Answer: A, B, C, or D

M2: ?
Answer: A, B, C, or D


So, the answer key could be: TTF - AB, FTT - AA, ...

For 3 true-false questions there are 2*2*2 = 8 combinations possible but since we are told that the correct answers to all true-false questions cannot be the same, then we should subtract the cases TTT and FFF, so for 3 true-false questions we get 8 - 2 = 6 combinations.

For 2 multiples-choice questions with 4 answer choices each there are 4*4 = 16 combinations possible.

Thus there are total of 6*16 ways a teacher can write an answer key for the quiz.

Answer: C.

Hope it's clear.
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didn't multiple choice questions have more than one ans choice
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ADisHere
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In how many ways can a teacher write an answer key for a min 29 Oct 2024, 14:39
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jlgdr
Actual way of solving this one is

2*2*2*4*4 all possible scenarios

2*1*1*4*4 unwanted scenarios

So it bouls down to 128 - 32 = 96

Answer is C as correctly stated above

Hope it helps!
Cheers!
J :)
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a more systematic way would be

2*1*1*1*4*4 unwanted scenarios ( 2 account for either all T or all F and the three 1's account for tf questions!
thanks for sharing this approach
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In how many ways can a teacher write an answer key for a min 03 Nov 2024, 04:46
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Shouldn't the question be how the STUDENTs can write the answers?
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In how many ways can a teacher write an answer key for a min 19 Apr 2026, 02:09
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