krishnasty wrote:

Encountered another question and dont know how to proceed:

Every morning, Casey walks from her house to the bus stop. She always travels exactly nine blocks from her house to the bus, but she varies the route she takes every day. (One sample route is shown). How many days can Casey walk from her house to the bus stop without repeating the same route?

to reach from start to end point one has to walk on 4 horizontal lines and 5 Vertical lines irrespective of the path chosen as only right and up movements are allowed.

Hence one of the possible route will be HHHHVVVVV

but another path could be VVHHVHHVV

i.e. all possible arrangements of these 9 letters HHHHVVVVV are different routes

the arrangements of these 9 letters can be represented by 9!/(5!*4!) which is same as 9C4 or 9C5

Alternatively we may say that out of 9 blank spaces we need to select only 4 places for H's which we can do in 9C4 ways and rest 5 places can be filled by V in just one way

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