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AP EAMCET202419 May 2024Evening ShiftMathematicsProbabilityActual

Out of first 5 consecutive natural numbers, if two different numbers x and y are chosen at random, then the probability that x^4-y^4 is divisible by 5 is

Options

  1. A2 5
  2. B4 5
  3. C3 5
  4. D1 5

Correct answer

C. 3 5

Step-by-step solution

We know, if two numbers x and y are choosen at random without replacement from the set 1,2,3,4, . . 5 K , then the probability that x^4-y^4 is divisible by 5 is 17 K-5 5(5 K-1) Given set = 1,2,3,4,5 K=1 So, required probability = 17 1-5 5(5 1-1) = 12 5 4 = 3 5 .

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