In an Examination, a candidate has to pass in each of the four subjects. In how many ways can be fail ?

Answer

To find the number of ways a candidate can fail in an examination where he must pass in each of the four subjects, we can approach the problem as follows:

### Step-by-Step Solution:

1. **Identify the Subjects**: The candidate has four subjects: Subject 1, Subject 2, Subject 3, and Subject 4.

2. **Determine Outcomes for Each Subject**: For each subject, the candidate has two possible outcomes: he can either pass or fail.

3. **Calculate Total Outcomes**: Since there are four subjects, and each subject has 2 outcomes (pass or fail), we can calculate the total number of combinations of outcomes across all subjects. This is done using the formula for combinations:
\[ \text{Total Outcomes} = 2 \times 2 \times 2 \times 2 = 2^4 = 16 \]

4. **Identify Failing Combinations**: However, the question specifically asks for the number of ways the candidate can fail. The candidate will fail if he does not pass all subjects. Since he must pass all four subjects to succeed, we can determine the failing combinations by excluding the single case where he passes all subjects.

5. **Calculate Failing Ways**: The only way he can pass is if he passes all four subjects, which is just 1 way. Therefore, the number of ways he can fail is:
\[ \text{Failing Ways} = \text{Total Outcomes} - \text{Passing Ways} = 16 - 1 = 15 \]

### Final Answer:
The candidate can fail in **15 different ways**.