N2008 P2 Q10

A group of diplomats is to be chosen to represent three islands, \(K\), \(L\) and \(M\). The group is to consist of \(8\) diplomats and is chosen from a set of \(12\) diplomats consisting of \(3\) from \(K\), \(4\) from \(L\) and \(5\) from \(M\). Find the number of ways in which the group can be chosen if it includes

1. \(2\) diplomats from \(K\), \(3\) from \(L\) and \(3\) from \(M\),[2]
2. diplomats from \(L\) and \(M\) only,[2]
3. at least \(4\) diplomats from \(M\),[2]
4. at least \(1\) diplomat from each island.[4]