Routes around Chicago
You take the train to Chicago for a summer concert at Harris Theater in Millennium Park. Since it’s nice out, you decide to walk from Union Station (at the corner of Canal and Adams) to the entrance to Millennium Park (at the corner of Randolph and Michigan Avenue). If you only walk East and North on the marked streets, how many possible routes are there to take?
Make a prediction about the number of routes you could take. What's a number that's too high and what a number that's too low?
Spend some time thinking about how you want to figure out the number of routes. When you're ready there's some hints below to help you.
You take the train to Chicago for a summer concert at Harris Theater in Millennium Park. Since it’s nice out, you decide to walk from Union Station (at the corner of Canal and Adams) to the entrance to Millennium Park (at the corner of Randolph and Michigan Avenue). If you only walk East and North on the marked streets, how many possible routes are there to take?
Make a prediction about the number of routes you could take. What's a number that's too high and what a number that's too low?
Spend some time thinking about how you want to figure out the number of routes. When you're ready there's some hints below to help you.
There are many ways to solve this problem. The hints below help you figure it out with two different methods that don't involve having to count every single route!
Hint 1 This hint will help you recognize a pattern that we'll use for other applications in Target B.
Hint 2 This hint shows you how you can use permutations to help solve the problem.
Solution