A city council consists of seven Democrats
and eight Republicans. If a committee of
seven people is selected, find the probability
of selecting three Democrats and four
Republicans.
step 1
we have seven Democrats------> select three Democrats
Find out 3C7
[tex]3C7=\frac{7!}{3!(7-3)!}=35[/tex]step 2
eight Republicans ------> select four Republicans
Find out 4C8
[tex]4C8=\frac{8!}{4!(8-4)!}=70[/tex]step 3
Total possible favorable outcomes
35*70=2,450
total possible outcomes
Find out 7C15
[tex]7C15=\frac{15!}{7!(15-7)!}=6,435[/tex]therefore
the probability is
P=2,450/6,435
simplify
