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JEE MainMathematicsProbability

A 3 -digit number is randomly selected. The probability that it contains exactly two prime digits is

Options

  1. A8 25
  2. B7 18
  3. C68 225
  4. D36 125

Correct answer

C. 68 225

Step-by-step solution

The total number of 3 -digit numbers is 9 10 10 = 900 . The prime digits in base 10 are 2, 3, 5, 7 (total 4 digits). The non-prime digits are 0, 1, 4, 6, 8, 9 (total 6 digits). Let P denote a prime digit and N denote a non-prime digit. For a 3 -digit number to have exactly two prime digits, the possible configurations are PPN , PNP , and NPP . Case 1: PPN The number of such numbers is 4 4 6 = 96 . Case 2: PNP The number of such numbers is 4 6 4 = 96 . Case 3: NPP The first digit must be a non-prime digit but cannot

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