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?

Guest Mar 28, 2019

#1**+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

killersteve27 Mar 28, 2019