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Math Help - How many 3 digit ...

  1. #1
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    How many 3 digit ...

    How many 3 digit numbers less than 500 can we form using the digits 1,2,3,4,5,6,7
    without REPETITION ?

    answer 1:
    starting from ones ---> (7)(6)(4) = 168

    answer 2:
    starting form hundreds ---> (4)(6)(5) = 120

    Which answer is correct ? and WHY ??
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  2. #2
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    Quote Originally Posted by razemsoft21 View Post
    How many 3 digit numbers less than 500 can we form using the digits 1,2,3,4,5,6,7
    without REPETITION ?
    answer 2:
    starting form hundreds ---> (4)(6)(5) = 120
    The number looks like HTD where H can be any one of 1,2,3,4.
    So how many choices do you now have for T~?
    Finish it.
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  3. #3
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    Quote Originally Posted by Plato View Post
    The number looks like HTD where H can be any one of 1,2,3,4.
    So how many choices do you now have for T~?
    Finish it.
    OK , but why method 1 doesn't work (starting for ones) 7*6 and the take the hundreds which is 4 and get 168 numbers
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  4. #4
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    Quote Originally Posted by razemsoft21 View Post
    OK , but why method 1 doesn't work (starting for ones) 7*6 and the take the hundreds which is 4 and get 168 numbers
    It does not work because it is wrong.
    The hundredth digit is restricted, so the other two are dependent on that choice.
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