Count all possible paths from top left to bottom right of a mXn matrix | PHP program to count all possible paths from top left to top bottom using combinatorics ; We have to calculate m + n - 2 C n - 1 here which will be ( m + n - 2 ) ! / ( n - 1 ) ! ( m - 1 ) ! ; Driver code
< ? php function numberOfPaths ( $ m , $ n ) { $ path = 1 ; for ( $ i = $ n ; $ i < ( $ m + $ n - 1 ) ; $ i ++ ) { $ path *= $ i ; $ path /= ( $ i - $ n + 1 ) ; } return $ path ; } { echo ( numberOfPaths ( 3 , 3 ) ) ; }