Permutation and Combination - Arrangements with Position or Pattern Restrictions

\(12\) students consisting of \(4\) from Class \(A\), \(5\) from Class \(B\) and \(3\) from Class \(C\) participate in a team bonding activity where they are divided into \(3\) groups of \(4\).

1. Find the number of ways such that each group has at most two students from Class \(A\).[3]

During lunchtime, all the students from Class \(A\) and Class \(B\) are seated at a round table with \(10\) chairs. Find the number of different seating arrangements if no two students from Class \(A\) are seated next to each other if the chairs are

2. all identical,[2]
3. numbered.[2]