Each question in a question paper has four choices for its answer out of which only one is correct. A candidate is to answer three questions. The number of ways he fails to give all answer correct is

Options

A. 64
B. 60
C. 61
D. 63

Answer

To solve the problem, we need to determine the number of ways a candidate can answer three questions incorrectly when each question has four choices, with only one correct answer.

### Step-by-Step Solution:

1. **Identify the Total Choices per Question**:
Each question has 4 choices for the answer.

2. **Identify the Correct Answer**:
Out of the 4 choices, only 1 is correct. Therefore, for each question, there are 3 incorrect choices.

3. **Calculate the Total Ways to Answer Three Questions**:
Since the candidate is answering 3 questions, and each question has 4 choices, the total number of ways to answer all three questions is:
\[ 4 \times 4 \times 4 = 4^3 = 64 \]

4. **Calculate the Number of Ways to Answer All Questions Correctly**:
There is only 1 way to answer all three questions correctly (by choosing the correct answer for each question).

5. **Calculate the Number of Ways to Fail to Answer All Questions Correctly**:
To find the number of ways the candidate fails to answer all questions correctly, we subtract the number of ways to answer all questions correctly from the total number of ways to answer the questions:
\[ \text{Ways to fail} = \text{Total ways} - \text{Ways to answer correctly} \]
\[ \text{Ways to fail} = 64 - 1 = 63 \]

Thus, the number of ways the candidate fails to give all answers correct is **63**.