Let X= 1,2,3,4,5 . The number of different ordered pairs (Y, Z) that can be formed such that Y X, Z X and Y Z is empty, is

Step-by-step solution

Y X , Z X Let a X , then we have following chances that (1) a Y, a Z (2) a Y, a Z (3) a Y, a Z (4) a Y, a Z We require Y Z= Hence (2), (3), (4) are chances for ' a ' to satisfy Y Z= . Y Z= has 3 chances for a . Hence for five elements of X , the number of required chances is 3 3 3 3 3=3^5