Answer to Question #258570 in Combinatorics | Number Theory for Arigato

Question

Using Polya's method

Consider the street map. Trisha wishes to walk directly from point A to point B. How many

different routes can she take if she wants to go past Starbucks on Third Avenue?

Answer 1

From Sturbucks to point B she has 3 direct routes: Sturbucks - Third Avenue - Crest Boulevard - Point B, Sturbucks - Third Avenue - Gateway Boulevard - Fourth Avenue - Point B, Sturbucks - Third Avenue - Park Avenue - Fourth Avenue -Point B .

From point A to Sturbucks she has also 3 direct routes: Point A - First Avenue - Board Walk - Third Avenue -Sturbucks , Point A - River Walk - Second Avenue - Board Walk - Third Avenue - Sturbucks, Point A - River Walk - Third Avenue - Sturbucks

So she can take:

$3\cdot3=9$ routes