Question

In Exercises 5–36, express all probabilities as fractions.

FedEx Deliveries With a short time remaining in the day, a FedEx driver has time to make deliveries at 6 locations among the 9 locations remaining. How many different routes are possible?

Short answer

The number of different routes possible is equal to 60480.

Step-by-step solution

Given information

Six deliveries at six different locations are to be made by the FedEx driver.

The different possible routes are to be computed.

Permutation

The total number of possible ways to choose r units from n units, when the order of the arrangements is considered, is computed using permutation.

${}^n{P}_r=\frac{n!}{\left(n-r\right)!r!}$

Calculation

The total number of locations is equal to 9.

The number of deliveries to be made is 6.

The total number of possible routes that can be taken to make the deliveries is equal to:

$$\begin{gathered} {}^9{P}_6=\frac{9!}{\left(9-6\right)!6!} \\ =60480 \end{gathered}$$

Therefore, the number of different routes possible to make the six deliveries is equal to 60480.