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A renewable energy consultant is assessing a wind farm with three turbines, each capable of producing energy in increments of 1, 2, or 3 units per hour. What is the probability that exactly two of the turbines produce 2 units of energy in a given hour?
Probability of a specific configuration:
Thus, the probability for any specific configuration where two turbines output 2 units and the third outputs either 1 or 3 is:
Multiply by the number of ways to choose the two turbines:
A paleobotanist is examining fossilized plant remains and categorizes each specimen based on two characteristics: leaf shape (either oval or oblong) and stem type (either woody or herbaceous). If the paleobotanist has 5 distinct leaf shapes and 3 distinct stem types, how many unique specimens can be formed by combining one leaf shape with one stem type?