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Math Help - 3 numbers picked from 1 - 10 prob lowest no is 5

  1. #1
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    3 numbers picked from 1 - 10 prob lowest no is 5

    I have the question you have the numbers 1 - 10 and 3 numbers are picked at random whats the probability the lowest picked number is 5

    What i guessed it would be is to use the choose functions so 10C1 * 4C1 * 3C1 / 10C3 which equals 1 which is wrong. But ive no idea how else to do it.
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  2. #2
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    Hello, renlok!

    You have the numbers 1 - 10 and three numbers are picked at random.
    What's the probability the lowest picked number is 5?
    Choosing three numbers from ten numbers, there are: . _{10}C_3 \:=\:{10\choose3} \:=\:120 outcomes.

    We want the "5" and two Others.
    The two Others are chosen from {6, 7, 8, 9, 10}.
    .There are: . _5C_2 \:=\:{5\choose2} \:=\:10 ways.

    Therefore: . P(\text{lowest is 5}) \;=\;\frac{10}{120} \;=\;\frac{1}{12}

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