Answer:
1/120 = 0.0083 = 0.83% probability that the inspector visits the restaurants in alphabetical order.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Arrangments of x elements:
The number of possible arrangments of x elements is given by:
[tex]A_{x} = x![/tex]
Desired outcomes:
Visiting all restaurants in alphabetical order, so only 1 possible outcome, which means that [tex]D = 1[/tex].
Total outcomes:
5 restaurants will be visited. The total number of orders is given by:
[tex]T = A_{5} = 5! = 120[/tex]
What is the probability that the inspector visits the restaurants in alphabetical order?
[tex]p = \frac{D}{T} = \frac{1}{120} = 0.0083[/tex]
1/120 = 0.0083 = 0.83% probability that the inspector visits the restaurants in alphabetical order.
