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How many ways are there to answer a 10-question true/false test, where at least 3 of the questions have been answered with a false?

 Mar 28, 2019
 #1
avatar+98 
+2

Total ways to answer 10 true or false questions = 2^10 = 1024

 

Let False =F, True = T, and C(n,r) means combination of r objects out of n objects.

 

Required ways = Total ways - 1F . 9T - 2F . 8T

 

= 1024 - C ( 10,1) - C ( 10,2)

 

= 1024 - 10 - 45 = 969 is the required answer

 Mar 28, 2019
 #2
avatar+4775 
+1

You omitted the case where all the questions were answered true, i.e. the C(10,0) case.

 

That brings the number to 1024 - 1 - 10 - 45 = 968

Rom  Mar 28, 2019
edited by Rom  Mar 28, 2019

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