GATE 2026 CS (CS1) – Question 6
Combinatorics deals with problems involving counting. For example, “How many distinct arrangements of N distinct objects in M 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:
P: Combinatorics is always invoked in the modeling of physical phenomena.
Q: 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 P and Q?
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Correct answer: (B) P is False and Q is True
Explanation
- Statement P asserts that combinatorics is *always* invoked. However, the passage states that this counting is *sometimes* used in the modeling of several physical phenomena. Thus, P cannot be inferred and is False.
- Statement Q asserts that modeling some physical phenomena involves assigning probabilities to combinatorial possibilities to compute average values. The passage explicitly says: 'Often, in such models, the different combinatorial possibilities are assigned probability values. Assigning probabilities enables the computation of the average values of physical quantities.' Thus, Q is directly supported and is True.
Therefore, P is False and Q is True, so option (B) is correct.