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A teacher has made ten statements for a True-False test. Four statements are true and six are false. However, no two true statements are consecutive.  How many distinct answer keys could there be for the test?

 Jun 15, 2021
 #1
avatar+35057 
+1

FOUR ways to keep the four  TRUES   separated in the line up of 10 questions

 

 |     |     |     |     |     |     |     |     |     |   

T         T          T         T                          This is one way.....then you can shift the line of trues to the right 3 more times    total   4 ways

 Jun 15, 2021
 #2
avatar+524 
0

Since the only condition is that no 2 trues are consecutive aren't there more than 4 ways to arrange them? 

amygdaleon305  Jun 15, 2021
 #3
avatar+35057 
0

You are correct.....

they could be separated like this : 

 

 

 |     |     |     |     |     |     |     |     |     |   

T               T               T         T                   

                 or other ways.....   let me think about how to derive the answer for a little while......If I come up with a solution I will let ya know !

 

 

THANX !  ~ EP

ElectricPavlov  Jun 15, 2021

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