Binomial coefficient for grid problem

#1

I was not able to grasp how n-1 and m-1 moves was transferred to use formula ( m-1 + n-1 ) ! / (m-1)! (n-1)! .
How we derived this formula . Is this using permutations formula with repeat if yes then what is analogy here ?

#2

Hey @nirmal1067 You need to take (n - 1) down steps (let’s say D), and (m - 1) right steps (let’s say R).

Now the total number of ways = number of ways to arrange (n - 1) D’s and (m - 1) R’s, which is simply

((n - 1) + (m - 1))! / ((n-1)! * (m-1)!)
#3

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