A Trip To Mordor

Frodo and Sam are attempting to carry the Ring of Power to Mordor to destroy, ridding Middle Earth of Evil. They must stop at multiple spots on their Journey to gather food and supplies. Shown on the map are all possible paths they may take from the Shire to Mordor. They may only follow the arrows in the direction they face.

• How many ways can they carry the ring from the Shire to Mordor?
• The Nazgul are in hot pursuit of Frodo and Sam. If the Nazgul starts at the Shire and randomly chooses a path to Mordor, what is the probability they take the exact same path as Sam and Frodo?
• Suppose the Nazgul were given a tip that Frodo and Sam were seen passing through Anfalas. What’s is the probability they take the exact same path as the ring bearer from the Shire to Mordor?

You may gain 50 XP by submitting your answers to Mr. Merrick