877.
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?
Exam Year(s)
GATE CS - 2026,
Answer: B
P is False and Q is True.
The passage says combinatorial counting is sometimes used in modeling physical phenomena. Statement P says it is always invoked, which goes beyond, and against, what the passage claims, so P is false.
Statement Q restates the last three sentences: in such models the combinatorial possibilities are assigned probability values, and this enables the computation of average values of physical quantities. Q is limited to 'some' phenomena, matching 'sometimes', so it is true.
Any option calling P true ignores the word 'sometimes', and calling Q false ignores the passage's explicit link between probabilities and averages.