Two teachers are interviewing top 6 students in FTRE exam, in two different subjects starting at the same time. Each teacher interviews for 15 minutes, the number of ways in which interview can be scheduled is

Options

A. 61
B. 5!
C. `44xx6!`
D. `265xx6!`

Answer

To solve the problem of scheduling interviews for 6 students by 2 teachers, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have 2 teachers interviewing 6 students simultaneously. Each teacher will interview all 6 students, and we need to determine the number of ways these interviews can be scheduled.

2. **Identifying the Total Interviews**:
Each teacher will interview the same set of 6 students. Therefore, we need to consider the arrangements of the students for each teacher.

3. **Calculating Arrangements for One Teacher**:
The number of ways to arrange 6 students for one teacher is given by the factorial of the number of students, which is \(6!\).

\[ 6! = 720 \]

4. **Considering Both Teachers**:
Since both teachers are interviewing simultaneously and independently, the arrangements for both teachers can be combined. Thus, the total arrangements for both teachers will be \(6!\) for Teacher 1 and \(6!\) for Teacher 2.

5. **Calculating Total Arrangements**:
The total number of ways to schedule the interviews is given by the product of the arrangements for both teachers:

\[ \text{Total Ways} = 6! \times 6! = 720 \times 720 = 518400 \]

6. **Final Answer**:
Therefore, the total number of ways in which the interviews can be scheduled is \(518400\).