the number of ways a doctor can make his rounds if he has 4 patients and he checks each patient once
To determine the number of ways a doctor can make his rounds while checking each patient once, we can use the concept of permutations.
In this case, we have 4 patients and the doctor needs to visit each patient once. So, the order in which the patients are visited matters.
The number of ways to arrange the 4 patients (P1, P2, P3, P4) is given by the formula for the permutation of 4 objects, which is:
n! / (n - r)!
where n is the total number of objects (patients) and r is the number of objects taken at a time (in this case, all 4 patients).
Therefore, the number of ways the doctor can make his rounds is given by:
4! / (4 - 4)! = 4! / 0! = 4! = 4 x 3 x 2 x 1 = 24
Hence, the doctor can make his rounds in 24 different ways.
To find the number of ways a doctor can make his rounds if he has 4 patients and he checks each patient once, we can use the concept of permutations.
When the doctor checks each patient, he needs to determine the order in which he visits them. Since he has 4 patients, he can start with any of them, then move on to any of the remaining 3 patients, and so on.
To calculate the number of ways, we can use the formula for permutations:
\(P(n, r) = \frac{n!}{(n-r)!}\)
In this case, n represents the total number of patients (4), and r represents the number of patients the doctor visits during his rounds (also 4, since he checks each patient once).
\(P(4, 4) = \frac{4!}{(4-4)!} = \frac{4!}{0!} = 4 \times 3 \times 2 \times 1 = 24\)
So, there are 24 ways for the doctor to make his rounds if he has 4 patients and he checks each patient once.
4P4 = 4!
This is just the number of permutations of 4 things.