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Math Help - Counting problems

  1. #1
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    Arrow Counting problems

    Can anyone please "check" my following questions answers...

    Q How many strings of four decimal digits

    a) do not contain the same digit twice
    my ans: 4 x 9^2
    b) end with an even digit
    my ans: 5 x 10^3
    c) have exactly three digits that are 9s

    my ans: 4 x 9

    Thanks for the help!
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  2. #2
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    Quote Originally Posted by robocop_911 View Post
    Can anyone please "check" my following questions answers...

    Q How many strings of four decimal digits

    a) do not contain the same digit twice
    my ans: 4 x 9^2
    b) end with an even digit
    my ans: 5 x 10^3
    c) have exactly three digits that are 9s

    my ans: 4 x 9

    Thanks for the help!
    a) do not contain the same digit twice:
    10 \cdot 9 \cdot 8 \cdot 7 = 5040

    b) end with an even digit: Your answer is correct.

    c) have exactly three digits that are 9's: Your answer is correct.
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  3. #3
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    [QUOTE=robocop_911;151794]Q How many strings of four decimal digits
    a) do not contain the same digit twice
    my ans: 4 x 9^2 NO
    b) end with an even digit
    my ans: 5 x 10^3 YES
    c) have exactly three digits that are 9s
    my ans: 4 x 9 YES
    Part (a) is a simple permutation: (10)(9)(8)(7). No repeated digits.
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  4. #4
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    [quote=Plato;151796]
    Quote Originally Posted by robocop_911 View Post
    Q How many strings of four decimal digits
    a) do not contain the same digit twice
    my ans: 4 x 9^2 NO
    b) end with an even digit
    my ans: 5 x 10^3 YES
    c) have exactly three digits that are 9s
    my ans: 4 x 9 YES
    Part (a) is a simple permutation: (10)(9)(8)(7). No repeated digits.
    Can you please explain why it won't be 4 x 9^2?
    From what I think, there are 4 places for the same digit to occur twice in a 4 decimal digit and the remaining 2 places can contain any remaining 9 digits!
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  5. #5
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    how did the answer come?

    Can anyone "check" my following question answer...
    Q How many strings of four decimal digits

    a) have exactly three digits that are 9s
    my ans: 4 x 9
    How come is it 4x9 can anyone explain me that?

    Thanks for the help!
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  6. #6
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    There are 4 places to put the 'other' digit and 9 possible choices for that digit.
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  7. #7
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    Quote Originally Posted by Plato View Post
    There are 4 places to put the 'other' digit and 9 possible choices for that digit.
    How come there are 4 places to put "other digits". We need to have "exactly" three 9s in the number!

    Are you taking complement of the sentence or something?
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  8. #8
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    X999
    9X99
    99X9
    999X
    Four places.
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