Acertain baseball team has 15 players. only nine can be on the field at a time. each of the nine players on the field has a distinct field position: pitcher, catcher, first baseman, second baseman, third baseman, short stop, left field, right field, or center field. assume for the moment that every player is qualified to play every position. now suppose that not every player can play in every position. the outfielders (left field, center field, right field) can play any outfield position, the infielders (1st base, 2nd base, 3rd base, short stop) can play any infield position, the pitchers can only pitch, and the catchers can only catch. suppose a certain team has 22 players, of whom 4 are catchers, 5 are outfielders, 6 are infielders, and 7 are pitchers. how many ways can the team assign field positions to 9 of the 22 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled?