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