MHB If he chooses randomly, how many ways can Akio form his starting lineup

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Akio can form his starting lineup by selecting players for six specific positions from a roster of 16 players. The discussion explores how to calculate the total number of unique lineups using the fundamental counting principle. Additionally, it examines the scenarios where Sidney is specifically chosen for the libero position and the overall probability of her selection as a starting player. The calculations involve determining the combinations and probabilities based on Akio's random selection process. Understanding these concepts helps in analyzing team formation strategies in volleyball.
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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.

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

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

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

d. If Akio just randomly chooses six players to start, without regard to who plays which position, what is the probability that Sidney gets chosen?
 
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a. If he chooses randomly, how many ways can Akio form his starting lineup?

How many choices does Akio have for the first position on the team? For the second...all the way down to the second? Can you use the fundamental counting principle to determine the number of unique lineups Akio can choose?
 

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