Understanding the Problem
To arrange 10 examination papers such that the best and the worst are not together, we can approach the problem systematically.

Step 1: Total Arrangements
- The total arrangements of 10 papers without any restrictions is given by \(10!\).
- Calculation:
\(10! = 3,628,800\)

Step 2: Arrangements with Restrictions
- To find the arrangements where the best and worst are together, we can treat them as a single unit or block.

Step 3: Treating Best and Worst as a Block
- This block can be arranged in 2 ways (Best-Worst or Worst-Best).
- Now, we have 9 units to arrange (the Best-Worst block + 8 other papers).
- The arrangements of these 9 units is \(9!\).
- Calculation:
\(9! = 362,880\)

Step 4: Total Arrangements with Best and Worst Together
- Total arrangements with Best and Worst together:
\(2 \times 9! = 2 \times 362,880 = 725,760\)

Step 5: Applying the Principle of Inclusion-Exclusion
- To find the arrangements where Best and Worst are NOT together, subtract the arrangements where they are together from the total arrangements:
\[
\text{Arrangements with Best and Worst NOT together} = 10! - (2 \times 9!)
\]
- Calculation:
\(3,628,800 - 725,760 = 2,903,040\)

Final Result
- The number of arrangements of the 10 examination papers such that the best and worst are not together is **2,903,040**.