In a test, students are required to answer eight out of twelve questions Find the number of ways if (a) a student choose to answer any eight questions, (b) a student must choose three questions out of first five questions?
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If they answer 4 of the first 5, there are ways to choose which, and then ways to choose the remainder. Thus, there are 5*35=175 ways to pick the 8 questions this way. Thus there are 35+175=210 total ways to choose 8 of the 12 questions such that they pick 4 of the first 5.
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