In a examination there are four multiple choice questions and each question has 4 choices. Number of ways in which a student can fail to get all answer correct is
(i) 256
(ii) 254
(iii) 255
(iv) 63

Options

A. 256
B. 254
C. 255
D. 63

Answer

To solve the problem, we need to determine the number of ways a student can fail to answer all questions correctly in an examination consisting of four multiple-choice questions, each with four choices.

### Step-by-Step Solution:

1. **Determine the Total Number of Ways to Answer the Questions:**
Each of the four questions has 4 choices. Therefore, the total number of ways to answer all four questions can be calculated as:
\[ \text{Total ways} = 4 \times 4 \times 4 \times 4 = 4^4 \]

2. **Calculate \(4^4\):**
\[ 4^4 = 256 \]
So, there are 256 total ways to answer the four questions.

3. **Identify the Number of Ways to Answer All Questions Correctly:**
There is only 1 way to answer all questions correctly (i.e., selecting the correct answer for each question).

4. **Calculate the Number of Ways to Fail to Get All Answers Correct:**
To find the number of ways a student can fail to get all answers correct, we subtract the one way of getting all answers correct from the total number of ways:
\[ \text{Ways to fail} = \text{Total ways} - \text{Ways to answer all correctly} = 256 - 1 = 255 \]

5. **Final Answer:**
The number of ways in which a student can fail to get all answers correct is \(255\).

### Conclusion:
The correct option is (iii) 255.