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?

Accepted Solution

Answer:The different possible routes are​ :                            181440Step-by-step explanation: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:[tex]n_P_r=\dfrac{n!}{(n-r)!}[/tex]Here we have: n=9and r=7Hence, the different possible routes are:[tex]9_P_7=\dfrac{9!}{(9-7)!}\\\\\\9_P_7=\dfrac{9!}{2!}\\\\\\9_P_7=181440[/tex]        Hence, the answer is:                   181440