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Math Help - probability help

  1. #1
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    probability help

    The digits 2, 3, 4, 7 and 8 are each used once to form a
    five-digit number. What is the probability that the tens
    digit is odd and the number is divisible by 4? Express your
    answer as a common fraction.
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  2. #2
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    Hello, sri340!

    The digits 2, 3, 4, 7 and 8 are each used once to form a
    five-digit number.
    What is the probability that the tens digit is odd and the number is divisible by 4?
    With a little Thought, the solution is quite straight forward.

    We have a 5-digit number and its tens digit is odd.
    There are only 2 choices for the odd digit.


    The tens digit is 3: . _ _ _ 3 _
    To be divisible by 4, the units digit must be 2.
    And the other 3 digits can be placed in 3! \:=\: 6 ways.

    The tens digit is 7:_ _ _ 7 _
    To be divisible by 4, the units digit must be 2.
    And the other 3 digits can be placed in 3! \:=\:6 ways.

    Hence, there are: . 6 + 6 \:=\:12 such numbers.


    Since there are 5! = 120 possible 5-digit numbers,
    . . The probabiity is: . \frac{12}{120} \:=\:\frac{1}{10}

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