How many ways can 8 people be seated in a round table if two specific          people need to sit together?

To solve this problem, we can use the concept of permutations in combinatorics. Here are the steps:

1. Consider the two specific people who need to sit together as one unit. Now, instead of 8 individuals, we have 7 units to arrange (6 individuals + 1 pair).

2. Since it's a round table, the number of arrangements (permutations) for these 7 units is (7-1)! = 6! = 720. This is because in a circular arrangement, we consider one point as a reference and arrange the others in relation to it, hence n-1.

3. However, the two specific people can switch seats with each other, so we have 2! = 2 ways to arrange them.

4. Therefore, the total number of ways to arrange 8 people around a round table with the condition that two specific people need to sit together is 720 * 2 = 1440 ways.