To solve the problem (assuming it asks for the number of linear permutations of 8 distinct people where two specific people sit next to each other), follow these steps:

Step 1: Treat the two specific people as a single unit

When two people must sit next to each other, we can consider them as one combined "block." This reduces the problem to arranging 7 units (the block + the remaining 6 people).

Step 2: Calculate permutations of the units

The number of ways to arrange these 7 units in a line is (7!)? Wait no—wait, no: the block can be placed in any of the adjacent positions in the linear arrangement. Wait, another way:

• For linear permutations: The two adjacent people can occupy positions (1-2), (2-3), ..., (7-8) → 7 possible positions for the block.
• The two people in the block can swap places → 2 ways to arrange them.
• The remaining 6 people can be arranged freely → (6!) ways.

Step 3: Compute the total number of arrangements

Multiply these together:
[7 \times 2 \times 6! = 7 \times 2 \times 720 = 10080]

Answer: (\boxed{10080})

作者声明:本文包含人工智能生成内容。