A certain baseball team has 16 players. Only nine can be on the field at a time.

Question

A certain baseball team has 16 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 Problem 1 How may ways are there to select nine of the 16 players to be on the field (without regard to which position each player will have)? (Q1) Problem 2 How many ways are there to assign field positions to a given set of nine players? (Q2) Problem 3 How many ways are there to fill the nine field positions from among the 16 players (taking account of the position each player will have)? (Q3)

Explanation / Answer

#1.
9 players from 16 can be selected in 16C9 = 11440 ways

#2.
Any player can be assigned to any position.
Hence required number of ways to do that 9! = 362880 ways

#3.
9 field positions from among the 16 players can be filled in 16C9 * 9! = 4151347200 ways

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