SOLUTION: There are 15 ‘True or False’ questions in an examination. In how many ways can a student do the examination if he or she can also choose not to answer almost 3 questions?

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Question 642859: There are 15 ‘True or False’ questions in an examination. In how many ways can a student do the examination if he or she can also choose not to answer almost 3 questions?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If the student answers all 15 questions, then there is only one way to do this.

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If the student skips one question, and exactly one question only, then there are 15 ways to do this (since there are 15 questions to skip).

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If the student skips two questions, then there are 15 C 2 = 15*14/2 = 105 ways to do this.


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If the student skips three questions, then there are 15 C 3 = 15*14*13/6 = 455 ways to do this.

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So if a student can skip at most 3 questions, then there are 1+15+105+455 = 576 different ways to do this.