Final answer:
There are 60 ways to assign seats to the students Aaron, Baron, and Caron in a classroom with 5 rows of desks and 5 desks per row, such that for each student there is at least one more student in the same row or column.
Step-by-step explanation:
To find the number of ways to assign seats to the students Aaron, Baron, and Caron, such that for each student there is at least one more student in the same row or column, we need to consider different cases:
Case 1: Aaron is seated in a row and Baron or Caron is seated in the same row or column:
- There are 5 rows to choose from for Aaron, and once he is seated, there are 4 different seats for Baron or Caron in the same row or column.
- Therefore, there are 5 * 4 = 20 ways to assign seats in this case.
Case 2: Aaron is seated in a column and Baron or Caron is seated in the same row or column:
- There are 5 columns to choose from for Aaron, and once he is seated, there are 4 different seats for Baron or Caron in the same row or column.
- Therefore, there are 5 * 4 = 20 ways to assign seats in this case.
Case 3: Aaron, Baron, and Caron are all seated in the same row:
- There are 5 rows to choose from, and once all three students are seated, there are 2 seats left for the remaining two students.
- Therefore, there are 5 * 2 = 10 ways to assign seats in this case.
Case 4: Aaron, Baron, and Caron are all seated in the same column:
- There are 5 columns to choose from, and once all three students are seated, there are 2 seats left for the remaining two students.
- Therefore, there are 5 * 2 = 10 ways to assign seats in this case.
Adding up the possibilities from all cases, we get a total of 20 + 20 + 10 + 10 = 60 ways to assign seats to the students.