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

Options

  1. A1 12
  2. B3 40
  3. C1 15
  4. D7 120

Correct answer

C. 1 15

Step-by-step solution

Three distinct natural numbers are chosen from 1 to 10 . n ( s )=10 c ₃ 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)= n(E) n(S) = 8 10₃ = 8 7! 3! 10! = 8 3 2 1 10 9 8 = 1 15

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