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counting and probability intermediate

Problem

If two numbers will be randomly chosen without replacement from , what is the probability that their product will be a multiple of 9? Express your answer as a common fraction.
Solution
There are possible pairs of numbers that can be chosen. None of these numbers are multiples of 9, so in order for their product to be a multiple of 9, both numbers must be a multiple of 3. The only possible pair that satisfies this is 3 and 6. Thus, the probability is
Final answer
\frac{1}{6}