Question 38

There are 47 players on the team.

To determine the total number of players on the team, we account for the overlaps among the different positions while ensuring that no player is counted more than once. By applying the principle of inclusion-exclusion, we can accurately calculate the unique players in each category.

A) 47

This option is correct. By using the inclusion-exclusion principle, the total number of unique players can be calculated as follows: Total = (Offense) + (Defense) + (Special Teams) - (Both Offense/Defense) - (Both Offense/Special) - (Both Defense/Special). Thus, Total = 25 + 28 + 17 - 7 - 3 - 13 = 47.

B) 48

This option is incorrect. If we were to assume there are 48 players, the calculation would not hold true as it would mean one additional player is being counted, which contradicts the given overlaps and the exclusion of players being counted in multiple roles.

C) 49

This option is incorrect. A total of 49 players would also imply an error in the counting of overlapping players, as it does not align with the inclusion-exclusion calculations that derive from the given player distribution.

D) 50

This option is incorrect. A total of 50 players suggests a miscalculation regarding the overlaps and unique counts among the offense, defense, and special teams categories, which have been precisely accounted for in the correct answer.

E) 51

This option is incorrect. Similar to the other incorrect options, 51 players would indicate an inflated count that fails to consider the overlaps appropriately, thus violating the principle of inclusion-exclusion.

Conclusion

The total number of players on the team is definitively 47, as calculated through the inclusion-exclusion principle. All other options fail to accurately represent the unique count of players based on the provided overlaps, leading to incorrect totals.