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A certain baseball team has 23 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.

Required:
How many ways are there to fill either the pitcher or catcher field position (but not both) from among the 23 players (leaving the other field positions empty)?

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Answer:

[tex]P \& C _{ways}=46ways[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=23[/tex]

Generally the pitcher or catcher field position can be filled in

23 way respectively

Where

No. ways for to fill Pitcher

[tex]P_{ways}=23 ways[/tex]

No. ways for to fill Catcher

[tex]C_{ways}=23 ways[/tex]

Therefore

Applying counting Principles

No. ways to fill both

[tex]P \& C _{ways}=23+23[/tex]

[tex]P \& C _{ways}=46ways[/tex]

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