SOLUTION: Please help, this problem is driving me crazy! An exam has 30 questions and students need to answer 20. How many ways can this be done if the first 5 and exactly 6 of the last

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Question 635791: Please help, this problem is driving me crazy!
An exam has 30 questions and students need to answer 20. How many ways can this be done if the first 5 and exactly 6 of the last 8 questions must be answered and question #13 must be skipped?
Thank you for your help!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
An exam has 30 questions and students need to answer 20. How many ways can this be done if the first 5 and exactly 6 of the last 8 questions must be answered and question #13 must be skipped?
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Answer 1st 5----1 way
Ans 6 of last 8---8C6 = 8C2 = 28 ways
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Need 9 more of the remaining 30-5-6-1 = 18 questions
Ans: 18C9 = 48620 ways
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Total # of ways to select 20: 1+28+45620 = 48649 ways.
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Note: I am assuming you are not asking for the number
of arrangements of the 20 questions.
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Cheers,
Stan H.