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If 4 distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all 4 of them are either divisible by 3 or divisible by 5 is

Options

  1. A6 C 4 100 C 4
  2. B33 C 4 100 C 4
  3. C20 C 4 100 C 4
  4. D47 C 4 100 C 4

Correct answer

D. 47 C 4 100 C 4

Step-by-step solution

Total cases = 100 C 4 Numbers which are divisible by either 3 or 5 = n 3 + n 5 - n 3 ∩ 5 = 33 + 20 - 6 = 47 Favourable cases = 47 C 4 Hence, required probability = 47 C 4 100 C 4

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