Probability of eating free lunch

Question

Three people go to a restaurant. Each of them has a chance to eat free if they roll the dice and win for the number they choose. Each person rolled the dice 2 times, first time for the main dish and the second time for the side dish. What is the probability that all 3 can win both the dishes?

Answer 1

If they are rolling one dice, then the probability of rolling their number is 1/6. So the probability of 3 people winning 2 times each is (1/6*1/6)*(1/6*1/6)*(1/6*1/6) = 1/46656

Answer 2

If the people are smart, they always choose a 7, as it has the highest probability. Then, the chance of rolling 6 7's will be (1/6)^6 = 1/46656 is approximately .0000214335 or