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  4. In an examination, there are three multiple choice questions and each question has 4 choices. Number of ways in which a student can fail to get all answers correct is

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Q. In an examination, there are three multiple choice questions and each question has $4$ choices. Number of ways in which a student can fail to get all answers correct is

Permutations and Combinations

Solution:

There are three multiple choice questions, each has four possible answers. Therefore, the total number of possible answers will be $4 \times 4 \times 4 = 64$. Out of these possible answers only one will be correct and hence the number of ways in which a student can fail to get all correct answers is $64 - 1 = 63$.