Question:
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
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
Updated On: Jul 6, 2022
- $11$
- $12$
- $27$
- $63$
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The Correct Option is D
Solution and Explanation
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 $64 - 1 = 63$.
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Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.