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21 April, 00:49

How many 3 digit numbers can be made if no digit is repeated and the number can not begin with a zero?

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Answers (2)
  1. 21 April, 01:16
    0
    We have to select 3 digits out of 10 with the following conditions:

    1) It can't start with 0

    2) repetition is not allowed.

    Let ABC this number:

    A = 9 choices (out of 10, excluding 0, because it can't be 0)

    B = 9 choices (out of 10 including 0, because it can be 0)

    C = 8 choices (out of 10 because 2 digits already selected)

    The total ways to write this number are:

    9 x 9 x 8 = 648 ways

    Another method:

    A can be written in ⁹C₁

    B can be written in ⁹C₁

    C can be written in ⁸C₁

    Total ways: ⁹C₁ x ⁹C₁ x ⁸C₁ = 648 ways
  2. 21 April, 03:24
    0
    digit #1 - 9 numbers (1-9)

    digit #2 = 9 numbers (0-9 minus the first digit)

    digit #3 = 8 numbers (0-9 minus the first 2 digits)

    9*9*8 = 648 combinations
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