The computers of six faculty members in a certain department are to be replaced. Two of the faculty members have selected laptop machines and the other four have chosen desktop machines. Suppose that...

The computers of six faculty members in a certain department are to be replaced. Two of the faculty members have selected laptop machines and the other four have chosen desktop machines. Suppose that only two of the setups can be done on a particular day, and the two computers to be set up are randomly selected from the six (implying 15 equally likely outcomes; if the computers are numbered 1, 2,…, 6, then one outcome consists of computers 1 and 2, another consists of computers 1 and 3, and so on).

1. What is the probability that both selected setups are for laptop computers?


2. What is the probability that both selected setups are desktop machines?


3. What is the probability that at least one selected setup is for a desktop computer?


4. What is the probability that at least one computer of each type is chosen for setup?