Consider the following maze a How many paths are there from

Consider the following maze.

a) How many paths are there from start to finish? I know this answer is C(9,4)

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

a)

that is incorrect because you have 4 rows and 6 columns so the answer will be 10C6 ( you always select the greater number)

b)

we have the total of ways that is 10C6 = 210

and we have only 6! / 4! = 30 ways that goes through the square with the star because we had 6 columns at the beggining but now we only have 4 columns if we start in the star

so the probability that a path goes through the square with the star is 30 / 210 = 0.142857