Question
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?
Official answer and solution
- Official answer
- B
- From
- Official GATE 2026 answer key
Solution
Check the quantifier in statement P ('always' vs. 'sometimes' in the passage) and verify statement Q against the last three sentences.
- Statement P is False: The passage explicitly states that combinatorial counting is sometimes used in the modeling of several physical phenomena, not always.
- Statement Q is True: The passage states that in such models of physical phenomena, combinatorial possibilities are often assigned probability values, which enables computing average values of physical quantities.
Option (B)
The answer is the one in the official GATE answer key. The solution is this site's own explanation.
Source
- Paper
- GATE 2026 Computer Science and Information Technology - Session 1 (CS1)
- Question
- 6 of 65
- Section
- General Aptitude
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