The answer key be designed to fit the criteria is 12 ways for Mrs.Wei
<u>Solution:
</u>
Given, Mrs. Wei was designing a 6 question True or False quiz.
She did not want there to be more than 2 answers the same in a row.
We have to find how many ways could the answer key be designed to fit the criteria?
Given that, more than 2 continuous answers are not allowed.
So, one answer same in a row conditions are t f t f t f or f t f t f t ⇒ 2 ways.
And, two answers same in a row conditions are
<em><u>Condition 1:</u></em>
t t f f t t t t f t f t t t f t t f
⇒3 ways by keeping 1st two answers same and constant and total 6 ways by interchanging true with false.
<em><u>Condition 2:</u></em>
f t t f f t f t t f t f
⇒ 2 ways by keeping 2nd two answers same and constant and total 4 ways by interchanging true with false.
<em><u>Condition 3:</u></em>
Next, f f t t f f ⇒ this is covered in 1st case when we interchange true with false.so, we are done with possibilities.
So, total ways are 2 + 6 + 4 = 12 ways.
Hence, there are 12 ways.
