The students in a class are seated according to the marks in the previous examination. Once it so happens that four of these students get equal marks and therefore the same rank. To decide their seating arrangement, the teacher wants to write down all possible arrangements, one in each of separate bits of paper, in order to choose one of these by lots. How many bits of paper are required ?

Answer

To solve the problem of how many bits of paper are required for the seating arrangements of the four students who received equal marks, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Problem**: We need to find the total number of arrangements for four students who have the same rank. Since they have the same marks, they are indistinguishable in terms of ranking.

2. **Understand Permutations**: The total number of arrangements (permutations) of 'n' indistinguishable objects is given by the formula \( n! \) (n factorial). Here, \( n \) is the number of students.

3. **Calculate Factorial**: In our case, we have \( n = 4 \) (the four students). Therefore, we need to calculate \( 4! \):
\[ 4! = 4 \times 3 \times 2 \times 1 \]

4. **Perform the Calculation**:
- First, calculate \( 4 \times 3 = 12 \)
- Next, calculate \( 12 \times 2 = 24 \)
- Finally, calculate \( 24 \times 1 = 24 \)

5. **Conclusion**: The total number of arrangements of the four students is \( 24 \). Therefore, the teacher will need to write down 24 bits of paper, each representing a different arrangement.

### Final Answer:
The number of bits of paper required is **24**.

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