UPSC NDA II 2023 Mathematics Solved Paper

Concept:Probability of two specific persons sitting together in a linear arrangement is found by treating them as a single unit, then multiplying by internal arrangements.Explanation:Total persons = 6 (P, Q, R, S, T, U).Total ways to arrange 6 in a row = $6!$.Treat Q and U as one block. This block plus the other 4 persons gives 5 units.Number of ways to arrange these 5 units = $5!$.Inside the block, Q and U can be arranged in $2!$ ways (Q-U or U-Q).So favorable outcomes = $5! \times 2!$.Probability = $\frac{5! \times 2!}{6!} = \frac{120 \times 2}{720} = \frac{240}{720} = \frac{1}{3}$.Answer:The probability that Q and U sit together is $\frac{1}{3}$.