Combinatorics deals with problems involving counting. For example, "How many distinct arrangements of distinct objects in spaces on a circle are possible?" is a typical problem in combinatorics. This kind of counting is sometimes used in the modeling of several physical phenomena. Often, in such models, the different combinatorial possibilities are assigned probability values. Assigning probabilities enables the computation of the average values of physical quantities.
Consider the following statements:
Combinatorics is always invoked in the modeling of physical phenomena.
Modeling some physical phenomena involves assigning probabilities to combinatorial possibilities in order to compute average values of physical quantities.
Based on the passage above, what can be inferred about statements and
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Answer: B
To determine the validity of statements P and Q, let us analyze the passage step-by-step:
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Statement P: "Combinatorics is always invoked in the modeling of physical phenomena."
The passage states: "This kind of counting is sometimes used in the modeling of several physical phenomena." Since it is only "sometimes" used, stating that it is "always" invoked is incorrect. Thus, P is False. -
Statement Q: "Modeling some physical phenomena involves assigning probabilities to combinatorial possibilities in order to compute average values of physical quantities."
The passage states: "Often, in such models, the different combinatorial possibilities are assigned probability values. Assigning probabilities enables the computation of the average values of physical quantities." Here, "such models" refers to the physical models using combinatorics. This directly supports the claim that modeling some physical phenomena involves assigning probabilities to compute average values. Thus, Q is True.
Therefore, P is False and Q is True, which corresponds to Option B.
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