Find the number of ways in which 5 boys and 4 girls can be arranged on a circular table such that no two girls sit together and 2 particular boys are always together?Options306288276296

To solve this problem, we need to use the principles of permutations and combinations. Here are the steps:

1. First, consider the 2 particular boys as a single entity. So, we now have 4 boys (including the entity) and 4 girls to arrange.

2. Since it's a circular arrangement, the number of ways to arrange n distinct items is (n-1)!. So, the 4 boys can be arranged in (4-1)!= 3! = 6 ways.

3. Now, we need to arrange the girls. Since no two girls can sit together, we can place them in the gaps between the boys. There are 4 gaps between the boys (including the one between the first and last boy).

4. The number of ways to arrange the 4 girls in 4 gaps is 4P4 = 4! = 24 ways.

5. The 2 particular boys can be arranged among themselves in 2! = 2 ways.

6. Therefore, the total number of ways to arrange the boys and girls is 6 (ways to arrange boys) * 24 (ways to arrange girls) * 2 (ways to arrange the 2 particular boys) = 288 ways.

So, the correct answer is 288.