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Two distinct numbers a and b are selected at random from 1,2,3, , 50 . The probability, that their product a b is divisible by 3, is

Options

  1. A272 1225
  2. B561 1225
  3. C664 1225
  4. D8 25

Correct answer

C. 664 1225

Step-by-step solution

Total ways = 50 2 = 1225 . ab is divisible by 3 iff at least one of a, b is divisible by 3. Multiples of 3 in 1, ,50 : 3,6, ,48 16 numbers. Non-multiples of 3: 34 . P( neither divisible by 3 ) = 34 2 50 2 = 561 1225 . P(ab divisible by 3 ) = 1 - 561 1225 = 664 1225 .

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