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Math Help - number of possibilities

  1. #1
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    number of possibilities

    how many 4 digit numbers can you form with (1,2,3,4,5,6,7) ? (No repeated numbers)

    The answer is 840 (7P4)

    BUT

    How many of these are odd numbers?

    I know that there are 4 odd numbers...
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  2. #2
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    Hello, Faisal2007!

    How many 4-digit numbers can you form with (1,2,3,4,5,6,7) ?
    (No repeated numbers)

    The answer is: . _7P_4 = 840

    But how many of these are odd numbers?

    The last (rightmost) digit must be odd; there are {\color{blue}4} choices: 1, 3, 5, or 7.

    The other three digits are chosen from the remaining six digits: . _6P_3 = {\color{blue}120} ways.


    Therefore, there are: . 4\cdot120 \:=\:480 odd numbers.

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  3. #3
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    Why is it 4 * 120 ?
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