jmc

If $a,$ $b,$ and $c$ are real numbers such that $a+b+c=4$ and $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=5,$ find the value of $$\frac{a}{b}+\frac{b}{a}+\frac{a}{c}+\frac{c}{a}+\frac{b}{c}+\frac{c}{b}.$$