Answer
$P(composed~of~all~Republicans)=\frac{45,379,620}{16,007,560,800}\approx0.002835$
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 45 distinct Republicans taken 7 at a time:
$N(composed~of~all~Republicans)=~_{45}C_7=\frac{45!}{7!(45-7)!}=\frac{45!}{7!\times38!}=\frac{45\times44\times43\times42\times41\times40\times39\times38!}{7\times6\times5\times4\times3\times2\times1\times38!}=45,379,620$
The number of combinations of 100 distinct individuals (55 Democrats and 45 Republicans) taken 7 at a time:
$N(S)=~_{100}C_7=\frac{100!}{7!(100-7)!}=\frac{100!}{7!\times93!}=\frac{100\times99\times98\times97\times96\times95\times94\times93!}{7\times6\times5\times4\times3\times2\times1\times93!}=16,007,560,800$
Using the Classical Method (page 259):
$P(composed~of~all~Republicans)=\frac{N(composed~of~all~Republicans)}{N(S)}=\frac{45,379,620}{16,007,560,800}\approx0.002835$
