10 students are to be seated in two rows equally for the MOCK CAT in a room. There are two sets of papers, code A and code B. Each of the two rows can have only one set of paper but different that from the other row. In how many ways these students can be arranged?

Options

A. 2775600
B. 1200560
C. 125600
D. 7259600

Answer

To solve the problem of arranging 10 students in two rows for the MOCK CAT, we can break down the solution into a series of steps.

### Step-by-Step Solution:

1. **Divide the Students into Two Rows**:
Since there are 10 students and we need to arrange them in two rows equally, we will have 5 students in each row.

2. **Choose Students for the First Row**:
We need to select 5 students out of the 10 to sit in the first row. The number of ways to choose 5 students from 10 can be calculated using the combination formula:
\[ \text{Number of ways to choose 5 from 10} = \binom{10}{5} = \frac{10!}{5!(10-5)!} = \frac{10!}{5!5!} = 252 \]

3. **Arrange Students in Each Row**:
After selecting 5 students for the first row, we can arrange these 5 students in that row. The number of arrangements for 5 students is given by:
\[ 5! = 120 \]
Similarly, the remaining 5 students will also be arranged in the second row, which also has:
\[ 5! = 120 \]

4. **Choose the Set of Papers**:
Each row can have one of the two sets of papers (code A or code B). Since the rows must have different sets of papers, we have 2 choices for the first row and 1 choice for the second row (the opposite of the first). Thus, there are:
\[ 2 \text{ choices for the first row} \]

5. **Calculate the Total Arrangements**:
Now, we can calculate the total number of arrangements by multiplying all the components together:
\[ \text{Total arrangements} = \binom{10}{5} \times 5! \times 5! \times 2 = 252 \times 120 \times 120 \times 2 \]

6. **Perform the Final Calculation**:
Let's calculate:
\[ 252 \times 120 = 30240 \]
\[ 30240 \times 120 = 3628800 \]
\[ 3628800 \times 2 = 7257600 \]

### Final Answer:
Thus, the total number of ways the 10 students can be arranged in two rows with different sets of papers is **7257600**.