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counting and probability intermediate

Problem

Tamika selects two different numbers at random from the set and adds them. Carlos takes two different numbers at random from the set and multiplies them. What is the probability that Tamika's result is greater than Carlos' result? Express your answer as a common fraction.
Solution
Tamika can get the numbers , , or . Carlos can get , , or . The possible ways to pair these are: , , , , , , , , . Four of these nine pairs show Tamika with a higher result, so the probability is .
Final answer
\frac{4}{9}