A drawer contains $9$ beads: four red beads, three blue beads and two green beads. In how many ways can we select five beads from the drawer with at least $2$ red, at least $1$ green, and an odd number of blue (beads of same color are identical)?
I know how to get $G(x)$ but don't know how to find the coefficient $x^5$. Any help would be great. Like where do I get for here?
$x_1$: choose red
$x_2$: choose blue
$x_3$: choose green
$G(x_1, x_2, x_3) = (x_1^2 + x_1^3 + x_1^4)(x_2^1 + x_2^2)(x_3^1 + x_3^3)$