1. ## 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?

2. 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.

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

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