Answer
$P(jury~of~all~faculty)=\frac{1}{34}\approx0.02941$
Work Step by Step
The order in which the individuals are selected does not matter and no individual can be selected more than once.
The number of combinations of 10 distinct students taken 5 at a time:
$N(jury~of~all~faculty)=~_{10}C_5=\frac{10!}{5!(10-5)!}=\frac{10!}{5!\times5!}=\frac{10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{5\times4\times3\times2\times1\times5\times4\times3\times2\times1}=\frac{10\times9\times8\times7\times6}{5\times4\times3\times2\times1}=252$
The number of combinations of 18 distinct individuals (8 students and 10 faculty) taken 5 at a time:
$N(S)=~_{18}C_5=\frac{18!}{5!(18-5)!}=\frac{18!}{5!\times13!}=\frac{18\times17\times16\times15\times14\times13!}{5\times4\times3\times2\times1\times13!}=\frac{1,028,160}{120}=8568$
Using the Classical Method (page 259):
$P(jury~of~all~faculty)=\frac{N(jury~of~all~faculty)}{N(S)}=\frac{252}{8568}=\frac{1}{34}\approx0.02941$
