Streets in a town form a grid. To get from home to school, Lalremsiami must walk 4 blocks east and 3 blocks north, in any order, never going west or south. How many different shortest routes can she take?

Explanation

1. 01

   Every shortest route is a string of 7 moves: 4 E's and 3 N's.

2. 02

   A route is fixed once you choose which 3 of the 7 moves are N.

3. 03

   Routes $= {}^{7}C_{3} = \frac{7 \times 6 \times 5}{6} = 35$.