Permutations: Calculating Nurse Visit Schedules - 9 Patients

The number of different ways the visiting nurse can visit the 9 patients, starting the first patient's visit at the beginning of the day, is given by the permutation formula:

$$9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 362,880$$

Therefore, there are 362,880 different ways the visiting nurse can visit the 9 patients in one day.