61-74 ■ Combinations These exercises involve counting combinations.
Jogging Routes A jogger jogs every morning to his health club, which is eight blocks east and five blocks north of his home. He always takes a route that is as short as possible, but he likes to vary it (see figure). How many different routes can he take ? [Hint: The route shown can be thought of as ENNEEENENEENE, where E is East and N is North.]
The number of different routes the jogger can take to reach the health club.
The jogger has to jogs blocks; East and North, in every possible combination.
First choose out of blocks east and then the out of then that would give the desired result.
The formula of the number of combinations as follows.
Here, is the total number of objects and is the number of objects chosen.
First, substitute for and for in equation as.
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started