In how many ways 5 boys sit round the table, so that two particular boys are next to each other?

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

1. Consider the two particular boys as a single entity. So now we have 4 entities to arrange (3 boys + 1 entity of 2 boys).

2. Since they are sitting in a round table, the number of arrangements is (n-1)!. So, the number of arrangements for 4 entities is (4-1)!= 3! = 321 = 6 ways.

3. However, the two particular boys can switch seats with each other. So, there are 2! = 2 ways for them to sit.

4. Therefore, the total number of ways for 5 boys to sit around the table so that two particular boys are next to each other is 6*2 = 12 ways.