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Math Help - probability

  1. #1
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    Exclamation probability

    a three member athletics council is to be randomly chosen from 10 students ,5 of whom are runners. The council positions are president , secretary and treasurer. Determine the probability that the eldest runner is president, send eldest runner is secretary and tried eldest runner is treasurer?
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  2. #2
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    Hello, someone21!

    A 3-member council is to be randomly chosen from 10 students, 5 of whom are runners.
    The council positions are President , Secretary and Treasurer.
    Determine the probability that the eldest runner is president,
    second eldest runner is secretary, and third eldest runner is treasurer.
    The ten athletes are: . R_1, R_2, R_3 and 7 others.

    . . \begin{array}{cc}\text{The probabiity that }R_1\text{ is chosen for President is:} & \dfrac{1}{10} \\ \\[-3mm]<br />
\text{The probability that }R_2\text{ is chosen for Secretary is:} &\dfrac{1}{9} \\ \\[-3mm]<br />
\text{The probability that }R_3\text{ is chosen for Treasurer is:} & \dfrac{1}{8} \end{array}

    The probability is: . \frac{1}{10}\cdot\frac{1}{9}\cdot\frac{1}{8} \;=\;\frac{1}{720}

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