Yesterday , i saw a question on this site.. I don't know where it went now..
It was as follows
Q. Find the number of ways of going from (0,0) to (m,n) given that one step can be :-
m,n>0
either 1 unit up
or 1 unit right
or √2 unit up-right along the diagonal
I made cases as follows :-
paths having only 1 diagonal step
paths having 2 diagonal steps..
paths having 3 diagonal steps and so on.. I summed all of them and got the answer as :-
$$\sum_{r=0}^{n} {m+n-r \choose n} {n \choose r}$$
But am unable to calculate this.. When i tried , The fact that the no. Of things to choose from was varying was of particular trouble. Two such problems(with variable things to choose from) i had done before involved the use of reduction formula of binomial coefficients.. But here i couldn't apply it.
Please help.. I would be grateful.
I am just a high school student.