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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 ├Ч 3 ├Ч 2 = 24. Total number of such 4-digit numbers = 3 ├Ч 24 = 72.

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