Three perfect dice D ₁, D ₂ and D ₃ are rolled. Let x, y and z represent the numbers on D ₁, D ₂ and D ₃ respectively. What is the number of possible outcomes such that x < y < z ?

Step-by-step solution

Let x, y, z are represent the numbers on three dice possible outcomes such that n < y < z aligned & =(1,2,3)(1,2,4),(1,2,5),(1,2,6),(1,3,4),(1,3,5) & (1,3,6),(1,4,5),(1,4,6),(1,5,6),(2,3,4),(2,3,5),(2, & 3,6),(2,4,5),(2,4,6),(2,5,6),(3,4,5),(3,4,6),(3,5, & 6),(4,5,6) & Total possible outcomes =20 aligned