A sales representative must visit five 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.
____choices
He has 5 choices for the first destination, 4 choices for the second, 3 for the third, 2 for the fourth and 1 for the last.
How many itineraries are possible?
its 120!
you hit the number 5 button on your calculator, then go to the math button then prob, then !.
so its gonna be 5!
To determine the number of different choices the sales representative has for the order in which to visit the cities, we can use the multiplication rule of counting.
The multiplication rule of counting states that if there are m ways to do one thing and n ways to do another thing, then there are m * n ways to do both things.
In this case, the sales representative must visit five cities. Let's label the cities as A, B, C, D, and E.
Using the multiplication rule of counting, the representative has:
- 5 choices for the first city to visit (A, B, C, D, or E)
- 4 choices for the second city to visit (as one city has already been visited)
- 3 choices for the third city to visit
- 2 choices for the fourth city to visit
- 1 choice for the fifth and final city to visit (as four cities have already been visited)
Therefore, the number of different choices the sales representative has for the order in which to visit the cities is: 5 * 4 * 3 * 2 * 1 = 120 choices.
So, there are 120 different choices for the sales representative to visit the cities in various orders.