If you are only allowed to move to the right or down how man

If you are only allowed to move to the right or down, how many possible routes are there from (S) to finish (F)? The are 8 total moves to make regardless of the route taken. {Hint: Consider the route as a sequence of letters R and D representing the direction of each move, and then use the permutations or combinations of something.} Please show all work and explain your methods.

Solution

There are 8 total moves to make regardless of the route! right!

A sample route maybe- RRDRDRDD..
here in all the places...any of (R,D) can be placed...we have 2 choices for each move...
It is important to note that...here ordering is important...(for example... RDDDDDDD is different from DDDDDDDR)..

we have 2 choices for each moves and we have 8 such moves!
So, possible no. of routes = (2 P 1)^8..= 256..