Two numbers are chosen from the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ at random. No repetition

Question

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]

Accepted Answer

(a)16 (b)0.821

2024 NYJC H1 Q7

2024 NYJC H1 Q7