  We extend our previous work on scattering amplitudes [1] to hadron
collisions. We provide a general formalism for the computation of eikonal
amplitudes squared for the radiation of soft and energy-ordered gluons off
three hard-legs at finite-N$_c$ to any order in the perturbative expansion.
Examples of three-hard legs processes include vector/Higgs boson production in
association with a single hard jet and dijet production in DIS. Explicit
expressions for the radiation of up to four gluons are provided as an
illustration of the formalism.
