We have to calculate m + n - 2 C n - 1 here which will be ( m + n - 2 ) ! / ( n - 1 ) ! ( m - 1 ) !
int path = 1 ; for ( int i = n ; i < ( m + n - 1 ) ; i ++ ) { path *= i ; path /= ( i - n + 1 ) ; } return path ; }