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

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• Phani
In summary, Akio coaches the girls volleyball team and needs to select players for the six different starting positions from his roster of 16 players. There are 16 choices for the first position, then 15 for the second, and so on, resulting in 16 x 15 x 14 x 13 x 12 x 11 = 5,184,000 possible lineups for Akio to choose from if he selects randomly. b. How many of those teams have Sidney playing in the libero position?In summary, there are 5,184,000 possible lineups that Akio can choose from if he selects randomly. If Sidney is chosen for the libero position, there are 15 choices for the first
Phani
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?

## 1. How many players are in Akio's starting lineup?

The number of players in Akio's starting lineup is not specified in the given question. Therefore, it can vary and the total number of ways to form the lineup will also vary accordingly.

## 2. Can Akio choose the same player multiple times for his starting lineup?

Yes, Akio can choose the same player multiple times for his starting lineup. This means that the number of ways to form the lineup will increase as Akio can have multiple combinations with the same player.

## 3. Is the order of players important in Akio's starting lineup?

No, the order of players is not important in Akio's starting lineup. The question specifies that the players are chosen randomly, so the order in which they are chosen does not affect the total number of ways to form the lineup.

## 4. What is the maximum number of players that can be in Akio's starting lineup?

The maximum number of players that can be in Akio's starting lineup is not specified in the given question. Therefore, it can vary and the total number of ways to form the lineup will also vary accordingly.

## 5. Can Akio have an empty starting lineup?

Yes, Akio can have an empty starting lineup. This means that he can choose not to have any players in his starting lineup. In this case, there is only one way to form the lineup, which is by choosing no players at all.

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