With a short time remaining in the day, a delivery driver has time to make deliveries at 7 locations among the 9 locations remaining. how many different routes are possible?

The different possible routes are :

                           181440

We are asked to find the number of different routes that are possible to choose  7 locations among the 9 locations remaining.

This means that we have to chose the locations and also we have to arrange them in different orders according to the different order of locations.

The method we have to use is a method of permutation.

When we have to chose and arrange r items out of a total of n items then the formula is given by:

Here we have: n=9

and r=7

Hence, the different possible routes are:

       Hence, the answer is:

                  181440

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: