There is a relationship between the number of cities one might
go to and the number of possible routes to get to those cities. For
example, the number of possible routes between three cities is two
routes; for four cities, there are six routes; for five cities,
there are twenty-four routes. You can observe a pattern here.
The table below shows that the number of routes forms a pattern in
relationship to the number of of cities. On the next page, your will learn how to select the
shortest route while planning for your trips. For additional
information of pattern in math, click here to go to the 'Pascal's
Triangle' page.
| Number of
Cities |
Number of Possible
Routes |
Pattern
A |
Pattern
B |
| 3 |
2 |
2! |
2 ´
1 |
| 4 |
6 |
3! |
3 ´
2 ´ 1 |
| 5 |
24 |
4! |
4 ´
3 ´ 2 ´ 1 |
| 6 |
120 |
5! |
5 ´
4 ´ 3 ´ 2 ´ 1 |
| 7 |
720 |
6! |
6 ´
5 ´ 4 ´ 3 ´ 2
´ 1 |
| 8 |
5,040 |
7! |
7 ´
6 ´ 5 ´ 4 ´ 3
´ 2 ´ 1 |
If Tom wants to go from Los Angeles to San Francisco, San Diego,
and Las Vegas, and back to Los Angeles again, how many possible
routes can he take?
Look at chart above. Four cities = six paths. He has six possible
routes.
David is going on a concert tour from his hometown of San Francisco
to Boston, New York, Los Angeles, Las Vegas, San Diego, Houston,
London, Tokyo, Hong Kong, and then Boise. He must return home at
the end of each concert to refill his suitcase with his things that
he needs. How many different routes can he travel to these
cities?
Estimate the answer:
 Less
than 10,000
Between 10,000 and 1,000,000
 More
than 1,000,000
|
