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NDA 1 2024 Maths, question 110

Topic: Probability

Q110

Three different numbers are selected at random from the first 1515 natural numbers. What is the probability that the product of two of the numbers is equal to third number ?

  1. (a) 191\frac{1}{91}
  2. (b) 2455\frac{2}{455}
  3. (c) 165\frac{1}{65}Correct answer
  4. (d) 6455\frac{6}{455}

Solution.

Answer: (c) 165\frac{1}{65}

  1. List distinct triples a < b < c ≤ 15 with ab = c: (2,3,6), (2,4,8), (2,5,10), (2,6,12), (2,7,14), (3,4,12), and (3,5,15).
  2. There are 7 favourable triples among C(15,3) = 455.
  3. The probability is 7/455 = 1/65, option (c).