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Math Help - Simple permutation problems

  1. #1
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    Simple permutation problems

    1.Find the numbers greater than 23000 that can be formed from the digits 1,2,3,4,5,6 without repeating any digit.

    2.how many 6 digit numbers can be formed without repeatig any digit from the digits 0,1,2,3,4,5?
    in how many of them will 0 be at tens place?


    3.Find the number of 5 digit numbers that can be formed from the digits 1,2,4,6,8 (when no digit is repeated) but

    i) the digits 2 and 8 are next to each other
    ii) the digits 2 and 8 are not next to each other


    Help will be appriciated.
    Last edited by hacker804; May 6th 2013 at 04:52 AM.
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  2. #2
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    Re: Simple permutation problems

    The first one: the number has to be greater than 23000. So the number at ten thousand place can be occupied by any one of the numbers, 2,3,4,5,6 That is in 5 ways.
    number at thousand place can be occupied by any one of the digits 3,4,5,6, that is in 4 ways The number at hundred place can be any one of the remaining 4 digits and tens place can be filled by any one of the remaining 3 digits and units place by remaining 2 numbers.
    So we have total numbers greater than 23000 is given by 5x4x4x3x2
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  3. #3
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    Re: Simple permutation problems

    Hello, hacker804!

    1.Find the numbers greater than 23,000 that can be formed
    from the digits {1, 2, 3, 4, 5, 6} without repeating any digit.

    There are a number of cases to consider.


    Five-digit numbers

    [1] The number begins with "23": . 2\;3\;\_\;\_\;\_\;\_
    . . .The other four digits can be arranged in 4! = 24 ways.

    [2] The number begins with "2": . 2\;\_\;\_\;\_\;\_\;\_
    . . .The second digit can be {4, 5, 6} . . . 3 choices.
    . . .The other four digits can be arranged in 4! = 24 ways.
    . . .Hence, there are:. 3\cdot24 \:=\:72 ways.

    [3] The first digit is not "2": 5 choices.
    . . .The other five digits can be arrnged in 5! = 120 ways.
    . . .Hence, there are:. 5\cdot5! \:=\:600 ways.

    Hence, there are:. 24 + 72 + 600 \:=\:696 five-digit numbers.


    Six-digit numbers

    There are:. 6! = 720 six-digit numbers.


    Therefore, there are:. 696 + 720 \:=\:1416 such numbers.
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