Counting A certain baseball team has 23 players. Only nine can be on the field a
ID: 3047214 • Letter: C
Question
Counting 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. Problem 4 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)? (Q4)Explanation / Answer
Lets say there are 23 positions empty, out of which either of first 2 are to be filled
Now, there can be 23C1 ways of choosing 23 people for position 1, please remember that according to the question we can't fill any other position ( including the catcher') when we fill the 1st. = 23 ways
Similarly, 2nd position can be filled in 23 ways. Rest all positions can't be filled at all. So, 23 ways
Hence, we can fill either of the positions in 23*23 = 529 ways
Answer is 529 ways