If three dice are rolled under the condition that no two dice show the same face, then what is the probability that one of the faces is having the number 6 ?

Step-by-step solution

Number of ways in which one of the face having the number 6 and no two dice show the same number. aligned & (1,2,6),(1,3,6),(1,4,6),(1,5,6),(2,3,6),(2,4,6),(2,5,6),(3,4, & 6),(3,5,6) . & Total favourable case =20+20+20=60 aligned Number of total output when three top faces of three dice shows different number =6 5 4=120 . Required probability = 60 120 = 1 2 .