Two different numbers are randomly selected from the set $\{1, 2, 3, 4\}$ and they are multiplied. What is the probability that the product is even? Express your answer as a common fraction.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Two different numbers are randomly selected from the set $\{1, 2, 3, 4\}$ and they are multiplied. What is the probability that the product is even? Express your answer as a common fraction.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\dfrac{5}{6}
Two different numbers are randomly selected from the set $\{1, 2, 3, 4\}$ and they are multiplied. What is the probability that the product is even? Express your answer as a common fraction.
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