Three dice are rolled. If the probability of getting different numbers on the three dice is p q , where p and q are co-prime, then q - p is equal to

Step-by-step solution

Given that three dice are thrown. The total number of outcomes when three dice are thrown together is 6 3 = 6 × 6 × 6 . The number of outcomes such that all the outcomes are different is = 6 × 5 × 4 . For ex: If the outcome in dice 1 is " 6 " then the number of outcomes for dice 2 should be 5   ( 1 , 2 , 3 , 4 , 5 ) which excludes the outcome " 6 " . Hence, the required probability is = 6 × 5 × 4 6 × 6 × 6 = 20 36 = 5 9 = p q ⇒ q - p = 9 - 5 = 4 The