Question

A sales representative must visit six 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

The number of different choices is 720.

Explanation:

The sales representative must visit six cities.

The visits of cities are independent.

Number of choices for the first visit: 6 possibilities

Number of choices for the second visit: 5 possibilities (He just visited one city, the sales representative don't have to go again)

Number of choices for the Third visit: 4 possibilities

Number of choices for the fourth visit: 3 possibilities

Number of choices for the Fifth visit: 2 possibilities

Number of choices for the Sixth visit: 1 possibilities

To count all the possibilities we have to multiple all of them:

6x5x4x3x2x1=720 different choices