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Previous Year Question (PYQs)

Three numbers are chosen from 1 to 20. Find the probability that they are consecutive.




Solution

Total ways = $\binom{20}{3} = 1140$ Consecutive triplets: (1,2,3), (2,3,4), …, (18,19,20) → 18 sets. Required probability $= \dfrac{18}{1140} = \dfrac{3}{190}$ $\boxed{\text{Answer: (D) }\dfrac{18}{\binom{20}{3}}}$

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