Permutation Combination : 001

Problem A1

How many paths are there from A to the line BC if the path does not go through any vertex twice and always moves to the left?

 

Answer

252

 

Solution

The simplest approach is to start with the vertices next to BC and to mark the number of paths for each, then move the vertices one further away, and so on.

2

  4

2   8

  4   16

2   8    32

  4   16    62

2   8    30    112

  4   14    50     182

2   6    20     70     252

  2    6    20      70    252