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      Question

      A 6-digit number is formed using the digits 1, 2, 3, 4, 5

      and 6. If each digit can be used only once, then find the probability that the number formed will be divisible by 4.
      A 4/15 Correct Answer Incorrect Answer
      B 1/6 Correct Answer Incorrect Answer
      C 2/5 Correct Answer Incorrect Answer
      D 3/8 Correct Answer Incorrect Answer
      E 1/4 Correct Answer Incorrect Answer

      Solution

      Total numbers formed = 6! = 720
      For divisibility by 4, the last two digits of the number must form a number divisible by 4
      From digits 1–6, valid 2-digit endings divisible by 4 without repetition are: 12, 16, 24, 32, 36, 52, 56, 64 → total = 8 combinations
      For each, remaining 4 digits can be arranged in 4! = 24 ways
      Total such numbers = 8 × 24 = 192
      Required probability = 192/720 = 4/15

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