#Basic Permuations and combination

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sand lake
scarlet valveBOT
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noble cryptBOT
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fractalfury

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vivid depot
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Total number of ways in which he can choose the three books to be borrowed 6+35=41

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Since each question has 4 options
i.e there are 4 choices or 4 ways to answer a question
∴ Number of ways to answer 3 questions is 4 × 4 × 4 = 64
Out of 64 ways, there is only one way which has all the answer correct.
So, number of ways in which a student fails to get all answer correct is 64 − 1 = 63 ways.

weak flume
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another way to calculate the first one is
-total amount of possibilities: 8C3 = 56
-amount of invalid possibilities: Math2 + 2 other books that are not Math1, which there are 6 of and needing to choose 2, so 6C2 = 15
56 - 15 = 41

sand lake
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Ty