Question

A sales representative must visit eight cities. There are direct air connections between each of the cities. Use the multiplication rule of counting to determine the number of different choices the sales representative has for the order in which to visit the cities.

Answer 1

Answer:

40,320 orders.

Step-by-step explanation:

By using the multiplication rule of counting, the sales representative has 8 choices for the first city, 7 choices for the second, 6 choices for the third, 5 choices for the fourth, 4 choices for the fifth, 3 choices for the sixth, 2 choices for the seventh, leaving just one city left to visit as the eight. Therefore, the number of different orders that the visits can be arranged is:

$n=8*7*6*5*4*3*2*1\\n=40,320\ orders$

There are 40,320 different possible orders.