Akio coaches the girls volleyball team. He needs to select players for the six different starting positions from his roster of $16$ players. On Akio’s teams, each position has its own special responsibility: setter, front left-side and middle hitters, back right- and left-side passers, and libero.  

1. If he chooses randomly, how many ways can Akio form his starting lineup?

   Hint (a):

   $_{16}P_6$

2. How many of those teams have Sidney playing in the libero position?

3. If Akio chooses starting teams randomly, what is the probability (in percent) that Sidney gets chosen as the starting libero?

   Hint (c):

   Relate your answers from parts (a) and (b) in a fraction to answer part (c).

4. If Akio just randomly chooses six players to start, without regard to who plays which position, what is the probability that Sidney gets chosen?

   Answer (d):

   $37.5$%