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

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SUMMARY

Akio can form his starting lineup for the girls volleyball team by selecting players for six distinct positions from a roster of 16 players. Using the fundamental counting principle, the total number of unique lineups is calculated as 16 choices for the first position, 15 for the second, and so on, resulting in 16!/(16-6)! = 524160 ways. If Sidney is fixed in the libero position, the number of lineups reduces to 15!/(15-5)! = 360360. The probability of Sidney being chosen as the starting libero is 1 in 16, or 6.25%. If Akio randomly selects six players without positional constraints, the probability of Sidney being included is 6 in 16, or 37.5%.

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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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