A fair coin is tossed once. If it shows head, then 2 fair dice are thrown simultaneously otherwise 3 fair dice are thrown simultaneously. The probability that all the dice show different numbers is k , then 180 k is equal to

Step-by-step solution

H → a fair coin shows head T → a fair coin shows tail A → 2 fair dice show unequal numbers B → 3 fair dice show unequal numbers Probability if all dice shows unequal number = P H . P A H + P T P B T = 1 2 × 6 × 5 6 × 6 + 1 2 × 6 × 5 × 4 6 × 6 × 6 = 5 12 + 5 8 = 15 + 10 36 = 25 36