Question

A government inspector must visit 5 restaurants to determine whether they are following proper food-handling and sanitation rules. All the restaurants have different names. If the inspector visits the restaurants in random order, what is the probability that the inspector visits the restaurants in alphabetical order

Answer 1

1/120 = 0.0083 = 0.83% probability that the inspector visits the restaurants in alphabetical order.

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:

`A_(x) = x!`

Desired outcomes:

Visiting all restaurants in alphabetical order, so only 1 possible outcome, which means that
`D = 1`.

Total outcomes:

5 restaurants will be visited. The total number of orders is given by:

`T = A_(5) = 5! = 120`

What is the probability that the inspector visits the restaurants in alphabetical order?

`p = (D)/(T) = (1)/(120) = 0.0083`

1/120 = 0.0083 = 0.83% probability that the inspector visits the restaurants in alphabetical order.