If $\alpha, \beta,\gamma$ are the roots of the equation $x^3-6x^2+11x-6=0$ and if $a= \alpha ^2+\beta^2+\gamma^2, \;b= \alpha \beta + \beta \gamma+ \gamma \alpha$ and $c= (\alpha+\beta)(\beta+\gamma)(\gamma+\alpha),$ then the correct inequality among the following is :

Question

$$\begin {array} {1 1} (1)\;a < b < c & \quad (2)\;b < a < c \\ (3)\;b < c < a & \quad (4)\;c < a < b \end {array}$$