At a dinner table 6 people, 3 men and 3 women, are to sit around the table.
a) How many different arrangements are possible?
b) Find the probability that two particular friends sit together.
c) How many ways can 3 particular people sit together?
d) What is the probability that all the boys are seated together?
e) What is the probability that the boys and girls alternate?
f) In how many ways can two people sit opposite each other?