Question

Each member of a baseball team has a specific position. Those positions are catcher, pitcher, infielder, and outfielder. At any given time, there must be nine players on the field: one catcher, one pitcher, four infielders, and three outfielders.

Answer 1

Create a roster for a baseball team of 25 players. Determine how many catchers, pitchers, infielders, and outfielders must be on the team.

How many catchers are on your team? _______3______

How many pitchers are on your team? _______3______

How many infielders are on your team? ______9______

How many outfielders are on your team? _____10____

How many different combinations of players can be on the field at any given time? Show your work. 25!/4!(25-4)!=25!/4!21!=12650

How many different permutations of players can be on the field at any given time? Show your work. 25!/(25-4)!=25!/21!=303600

Which of these numbers would be more helpful to a manager who wants to figure out who to play together on the field? Explain your answer. I think combinations because you combine the players with different players at different times.

If a major league baseball team plays 162 games in a season and 1 combination is used per game, how many seasons would it take to go through every combination of players? Explain your answer. Divide the combinations of players and divide it by the number of games we get aprox 78 seasons

How many seasons would it take to go through each permutation of players? Explain your answer. Divide the number of permutations of players by the number of games and we get approx 1874