Question

visiting nurses how many different ways can a visiting nurse visit 7 patients if she wants to visit them all in one day? there are \square different ways to visit 7 patients in one day.

Explanation:

Step1: Identify the problem type

This is a permutation problem where we need to find the number of ways to arrange 7 patients (since the order of visiting matters). The formula for permutations of \( n \) distinct objects is \( n! \) (n factorial), which is \( n\times(n - 1)\times(n - 2)\times\cdots\times1 \).

Step2: Calculate \( 7! \)

We calculate \( 7! \) as follows:
\( 7! = 7\times6\times5\times4\times3\times2\times1 \)
First, \( 7\times6 = 42 \)
Then, \( 42\times5 = 210 \)
Next, \( 210\times4 = 840 \)
Then, \( 840\times3 = 2520 \)
Next, \( 2520\times2 = 5040 \)
Finally, \( 5040\times1 = 5040 \)

Answer:

5040