SOLUTION: A teacher will take 10 questions from a study guide of 20 questions for a quiz. If a student knows the answer to 15 of the questions, what is the probability that student will get

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Question 171110: A teacher will take 10 questions from a study guide of 20 questions for a quiz. If a student knows the answer to 15 of the questions, what is the probability that student will get:
all 10 questions correct?
exactly 8 questions correct?
at least 9 questions correct?
I was able to solve the first question, the answer being (21/1292) by evaluating 15(nCr)10 / 20(nCr)10, but I have no idea how to do the other two questions. Even after I was given the answers, I couldn't figure out how to get to them.
Answer to second one is (225/646)
Answer to third one is (49/323)
Please Help!
Answer by oscargut(2103) (Show Source):
You can put this solution on YOUR website!
2nd) P(8 correct) is (15(nCr)8)(5(nCr)2) / 20(nCr)10
3rd) P(at least 9)=P(9 correct)+P(10 correct)
=[(15(nCr)9)(5(nCr)1)+ (15(nCr)10)] / 20(nCr)10