### Instruction: If two numbers will be randomly chosen without replacement from $\{3, 4, 5, 6\}$, what is the probability that their product will be a multiple of 9? Express your answer as a common fraction.### Response: To find the probability, I need to count the number of favorable outcomes and divide by the total number of possible outcomes.
The total number of ways to choose two numbers from a set of four without replacement is $\binom{4}{2} = 6$.
I can list them as follows: $(3, 4), (3, 5), (3, 6), (4, 5), (4, 6), (5, 6)$.
I notice that the only way to get a product that is a multiple of 9 is to have both factors be multiples of 3.
So, the only favorable outcome is $(3, 6)$.
Therefore, the probability is $\frac{1}{6}$.