Three distinct natural numbers chosen at random from 1 to 10. What is the probability that they are consecutive?

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NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. 1/12
  2. 3/40
  3. 1/15
  4. 7/120

Answer (Detailed Solution Below)

Option 3 : 1/15
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Explanation:

⇒n(S) = 10C3

Favourable outcomes = (1, 2, 3), (2, 3, 4), (3, 4, 5), (4, 5, 6), (5, 6, 7), (6, 7, 8), (7, 8, 9), (8, 9, 10)

⇒n(E) = 8

⇒ P(E) = \(\frac{n(E)}{n(S)} = \frac{8}{^{10}C_3}\)

\(\frac{8\times3\times2\times1}{10\times9 \times8} =\frac{1}{15}\)

∴ Option (c) is correct

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