An instructor gives an exam with twenty questions. Students are allowed to choose any fifteen questions to answer. (a) How many different choices of fifteen questions are there? (b) Suppose nine questions require coding and eleven do not. (i) How many groups of fifteen questions contain seven that require coding and eight that do not? (ii) How many groups of fifteen questions contain at most eight that require coding? (c) Suppose the exam instruction specifies that at most one of questions 1 and 2 MAY BE included among the fifteen. How many different choices of fifteen questions are there?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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An instructor gives an exam with twenty questions. Students are allowed to choose any fifteen
questions to answer.
(a)
How many different choices of fifteen questions are there?
(b)
Suppose nine questions require coding and eleven do not.
(i)
How many groups of fifteen questions contain seven that require coding and
eight that do not?
(ii)
How
many groups of fifteen questions contain at most eight that require coding?
(c)
Suppose the exam instruction specifies that at most one of questions 1 and 2 MAY BE
included among the fifteen. How many different choices of fifteen questions are there?
(d)
Suppose the exam instruction specifies that either both questions 1 and 2 are to be
included among the ten or neither is to be included. How many different choices of ten
questions are there?
Transcribed Image Text:An instructor gives an exam with twenty questions. Students are allowed to choose any fifteen questions to answer. (a) How many different choices of fifteen questions are there? (b) Suppose nine questions require coding and eleven do not. (i) How many groups of fifteen questions contain seven that require coding and eight that do not? (ii) How many groups of fifteen questions contain at most eight that require coding? (c) Suppose the exam instruction specifies that at most one of questions 1 and 2 MAY BE included among the fifteen. How many different choices of fifteen questions are there? (d) Suppose the exam instruction specifies that either both questions 1 and 2 are to be included among the ten or neither is to be included. How many different choices of ten questions are there?
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