Answer:
607 students are needed to ensure that there are two students with the same professor who received identical final examination scores.
Step-by-step explanation:
This question exemplifies the Pigeonhole principle.
The initial step involves determining the number of boxes and objects:
Each score corresponds to a box which contains the student who achieved that score.
If there were solely one professor grading, you would need 101+1 = 102 students to guarantee that there are two students with the same professor who received the same final examination score.
Nevertheless, considering every student, there are six professors, resulting in six combinations for any score.
Thus, a minimum of 6*101+1 = 607 students should be present to ensure that at least two students with the same professor received the same score on the final examination.
