A secretary works in a building located 9 block east abd 8bl

A secretary works in a building located 9 block east abd 8blocks north of his home. Every day he walks 17 blocks to work. Using a 19 times 18 grid: a. How many different routes are possible for him?

Solution

suppose we assume to go north ,he has to take upper direction (u)

and to go east he ahs to take right direction. (r)

since there are 17 steps out of which 9 are right (r) and 8 are upper (u)

so the number of routes = number of ways we can arrange 9 r and 8 u.

by using the concept of permutation and combination ,we get

17!/(8!*9!) = 24310