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How many different 3 digit numbers less than 500 can be made using the digits 3, 4, 5, and 6 if the digits can be used only once

  • math -

    Number of choices for the first digit = 4
    Since there cannot be repetitions,
    Number of choices for the second digit = 3
    Number of choices for the third digit = 2

    By the multiplication principle, the number of different 3-digit numbers with distinct digits that can be made from 4
    = 4*3*2 = ?

  • math -

    However, not all of those numbers are less than 500.

    choices for 1st digit: 2 (3 or 4)
    choices for 2nd digit: 3
    choices for 3rd digit: 2

    so, there are really only 12 possible numbers less than 500

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