2024 NYJC H1 Q7

Two numbers are chosen from the set \(\{1, 2, 3, 4, 5, 6, 7, 8, 9\}\) at random. No repetition of numbers is allowed. Find the number of different ways the two numbers can be chosen such that the difference of the two numbers is even.[3]

Amy chooses three numbers from the set \(\{0, 1, 2, 3, 4, 5, 6, 7\}\) at random and without replacement. Independently, Brandon also chooses three numbers from the set \(\{0, 1, 2, 3, 4, 5, 6, 7\}\) at random and without replacement. Find the probability that the numbers chosen by Amy and the numbers chosen by Brandon have at least one number in common.[3]