Please solve ALL a b parts of this question Justify your ans

Please solve ALL (a) (b) parts of this question. Justify your answers.

Let\'s assume that Tom is located at the bottom left corner of the maze below, and Jerry is located at the top right corner. Tom of course wants to get to Jerry by the shortest path possible. How many such shortest paths exist? How many shortest paths pass through the edge labelled X?

Solution

a) in n*n grid ,

number of shortest path = 2nCn

so here n = 9

so answer is 18 C 9

for better understanding ,you can visit

https://betterexplained.com/articles/navigate-a-grid-using-combinations-and-permutations/

b) shortest path that passes through edge X is

(6C3) * (11C5)

because first we have to reach left most point of edge X that is (6C3) {here n = 3}

now from right edge to right most top corner , there are 5 H and 6 V ,

so number of ways = (5 + 6)C5 = 11 C5

hence solution is (6C3) * (11C5)