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)?

Step-by-step explanation:

From the question we are told that:

Sample size

Generally the pitcher or catcher field position can be filled in

23 way respectively

Where

No. ways for to fill Pitcher

No. ways for to fill Catcher

Therefore

Applying counting Principles

No. ways to fill both

a4 - 3a2 - 1

step-by-step explanation:

step   1   :

equation at the end of step   1   :

  ((a4) -   3a2) -   1

step   2   :

trying to factor by splitting the middle term

2.1     factoring   a4-3a2-1  

the first term is,   a4   its coefficient is   1 .

the middle term is,   -3a2   its coefficient is   -3 .

the last term, "the constant", is   -1