Consider the following maze A player can only move right or

Consider the following maze. A player can only move right or down.

a) How many paths are there from start to finish?

b) If each path is equally likely to occur, what is the probability that a path goes through the square with the star?

Please show all work and explain your methods.

Solution

we have 5 rows and 6 columns in total 6+5 = 11

so there are 11! / (5! * 6! ) = 462

for the star we have 5! / 2! = 60

there are 5 rows in total , and there are only 2 rows from the star to the end

the probability is 60 / 462 = 0.1299