In a ballroom dance class, participants are divided in couples for each drill session. One partner leads and other follows for three minutes, and then the couple switches roles for next three minutes.
a) Only four people show up on time. How many manners are there to pair them up?
b) If instead six people show up on time, how many manners are there to pair them up?
c) Suppose all m people in the class arrive on time. (There are an even number of people in the class.) How many ways are there to pair them up?