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Math Help - Probability

  1. #1
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    Probability

    A three digit numberal with no repeated digits is made from the digits 1 throguh 7. What is the probability that the number indicated is:


    odd:

    7*6*4

    A multiple of 5:

    7*6*1


    Between 300 and 500

    2*6*5

    Between 300 and 600

    4*5*5


    thats what i think it is but I doubt they're right so could anyone help me please?
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  2. #2
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    Hello, lax600!


    A three-digit number with no repeated digits is made from the digits 1 through 7.
    There are: . 7\!\cdot\!6\!\cdot\!5\:=\:210 possible numbers.

    what is the probability that the number indicated is:
    (a) odd
    The last digit must be odd; there are {\color{blue}4} choices: . \{1,3,5,7\}
    The first two digits are chosen from the remaining 6 digits: . 6\!\cdot\!5\:=\:{\color{blue}30} ways.
    . . Hence, there are: . 4 \times 30 \:=\:120 odd numbers.

    Therefore: . P(\text{odd}) \;=\;\frac{120}{210}\;=\;\boxed{\frac{4}{7}}



    (b) A multiple of 5
    The last digit must be 5: one choice.
    The first two digits are chosen from the remaining 6 digits: . 6\!\cdot\!5\:=\:{\color{blue}30} ways.
    . . Hence, there are: . 1\!\cdot\!30\:=\:30 multiples of 5.

    Therefore: . P(\text{multiple of 5}) \;=\;\frac{30}{210} \;=\;\boxed{\frac{1}{7}}



    (c) Between 300 and 500

    The first digit must be 3 or 4: {\color{blue}2} choices.
    The last two are chosen from the remaining 6 digits: . 6\!\cdot\!5\:=\:{\color{blue}30} ways.
    . . Hence, there are: . 2\!\cdot\!30 \:=\:60 numbers between 300 and 500.

    Therefore: . P(\text{between 300 and 500}) \;=\;\frac{60}{210} \;=\;\boxed{\frac{2}{7}}



    (d) Between 300 and 600

    The first digit must be 3, 4, or 5: 3 choices.
    The last two digits are chosen from the remaining 6 digits; . 6\!\cdot\!5\:=\:{\color{blue}30} ways.
    . . Hence, there are: . 3\!\cdot\!30 \:=\:90 numbers bewteen 300 and 600.

    Therefore: . P(\text{between 300 and 6 00}) \:=\;\frac{90}{210} \;=\;\boxed{\frac{3}{7}}

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  3. #3
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    t ty
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