The number of arrangements is an illustration of permutations.
The number of arrangement is 5040
The given parameter is:
[tex]n = 7[/tex] --- number of days
[tex]r = 7[/tex] --dinners for 7 days
So, the number of different arrangement is
[tex]^nP_r = \frac{n!}{(n - r)!}[/tex]
Substitute known values
[tex]^7P_7 = \frac{7!}{(7 - 7)!}[/tex]
[tex]^7P_7 = \frac{7!}{0!}[/tex]
[tex]^7P_7 = \frac{5040}{1}[/tex]
[tex]^7P_7 = 5040[/tex]
Hence, the number of arrangement is 5040
Read more about arrangements at:
https://brainly.com/question/15301090
