2022 RI J2 CT Q8

A group of hikers is to be chosen to represent three hiking teams in an annual hiking challenge. The group is to consist of \(7\) hikers and is chosen at random from a set of \(10\) hikers consisting of \(2\) hikers from team \(A\), \(3\) hikers from team \(B\) and \(5\) hikers from team \(C\).

Find the number of ways in which the group can be chosen if

1. there are no restrictions,[1]
2. there are at least \(4\) hikers from team \(C\),[2]
3. there is at least \(1\) hiker from each team.[3]