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NDA 2 2024 Maths, question 103

Topic: Probability

Q103

Three distinct natural numbers are chosen at random from 11 to 1010. What is the probability that they are consecutive?

  1. (a) 1/121/12
  2. (b) 3/403/40
  3. (c) 1/151/15Correct answer
  4. (d) 7/1207/120

Solution.

Answer: (c) 1/151/15

  1. There are C(10,3)=120 equally likely three-element selections.
  2. Consecutive triples start at 1,2,…,8, giving 8 favourable selections.
  3. The probability is 8/120=1/15.