People exposed to a virus become sick 60% of the time. If 6 people are exposed to the virus, what is the probability exactly 4 of them get sick?
+118723 $$6C4(0.60)^4(0.40)^2$$
$${\left({\frac{{\mathtt{6}}{!}}{{\mathtt{4}}{!}{\mathtt{\,\times\,}}({\mathtt{6}}{\mathtt{\,-\,}}{\mathtt{4}}){!}}}\right)}{\mathtt{\,\times\,}}{{\mathtt{0.6}}}^{{\mathtt{4}}}{\mathtt{\,\times\,}}{{\mathtt{0.4}}}^{{\mathtt{2}}} = {\frac{{\mathtt{972}}}{{\mathtt{3\,125}}}} = {\mathtt{0.311\: \!04}}$$
.+118723 $$6C4(0.60)^4(0.40)^2$$
$${\left({\frac{{\mathtt{6}}{!}}{{\mathtt{4}}{!}{\mathtt{\,\times\,}}({\mathtt{6}}{\mathtt{\,-\,}}{\mathtt{4}}){!}}}\right)}{\mathtt{\,\times\,}}{{\mathtt{0.6}}}^{{\mathtt{4}}}{\mathtt{\,\times\,}}{{\mathtt{0.4}}}^{{\mathtt{2}}} = {\frac{{\mathtt{972}}}{{\mathtt{3\,125}}}} = {\mathtt{0.311\: \!04}}$$
