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An exam has 10 T/F questions. If a student guesses on all questions, what is the probability that he will get exactly 7 of them correct?
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Total number of outcomes 2^10.
To have exactly 7 questions answeared correctly student must have exactly 7 correct answears and exactly 3 incorrect. Total number of favorable outcomes 7C10 = 3C10.
P = 3C10 / 2^10 = 10!/(3!*7!2^10) = (5*3*2^3) / 2^10 = (5*3)/2^7 = 15/128
To have exactly 7 questions answeared correctly student must have exactly 7 correct answears and exactly 3 incorrect. Total number of favorable outcomes 7C10 = 3C10.
P = 3C10 / 2^10 = 10!/(3!*7!2^10) = (5*3*2^3) / 2^10 = (5*3)/2^7 = 15/128
I don't get it. I found 1/(2)7 but obviously I am wrong because there are many ways to get 7 good answers, not just one 
