N2016 P2 Q7

The management board of a company consists of \(6\) men and \(4\) women. A chairperson, a secretary and a treasurer are chosen from the \(10\) members of the board. Find the number of ways the chairperson, the secretary and the treasurer can be chosen so that

1. they are all women,[1]
2. at least one is a woman and at least one is a man.[3]

The \(10\) members of the board sit at random around a table. Find the probability that

3. the chairperson, the secretary and the treasurer sit in three adjacent places,[3]
4. the chairperson, the secretary and the treasurer are all separated from each other by at least one other person.[3]