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      Question

      How many 4-digit numbers greater than 3000 can be formed

      using the digits 1, 2, 3, 4, 5 without repetition?
      A 55 Correct Answer Incorrect Answer
      B 72 Correct Answer Incorrect Answer
      C 69 Correct Answer Incorrect Answer
      D 27 Correct Answer Incorrect Answer

      Solution

      We must form 4-digit numbers with digits from {1,2,3,4,5}, no repetition, and number > 3000. Thousands digit can be 3, 4, or 5 (3 choices). For each choice of thousands digit, we need to choose and arrange 3 more digits from the remaining 4 digits. Number of ways for remaining 3 places = P(4, 3) = 4 × 3 × 2 = 24. Total number of such 4-digit numbers = 3 × 24 = 72.

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