Suppose you live 8 blocks from where you work, and the blocks are square as shown
below. How many different 8 block routes are there from home to work ?
Starting at home you can choose to go up or to the right. After going one block
from home, you again have a choice of going up or to the right. Continuing
until you get to work, there are a total of 8 choices. Four choices must
be up and four to the right. So, the number of different routes is: