Question 1082467
I assume the problem means exactly 6, and not "6 or more":

{{{ (0.25)^6 *(0.75)^14 * 20C6 = 0.1686 }}} or  16.9 % 

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{{{ (0.25)^6*(0.75)^14 }}} represents one instance of getting 6 questions correct out of 20 (say the first 6 correct and the remaining 14 incorrect).
20C6  is the number of arrangements of those 6 correct answers out of a field of 20 questions