How to calculate the invariant amplitude for a decay process using wick's theorem?

I have difficulties to apply Wick’s theorem to the following problem-set:

We have three free scalar fields $phi_1, phi_2, phi_3$. While the field $phi_3$ has the mass $M$ while $phi_1$ and $phi_2$ are massless. With the interaction Hamiltonian:
$$
H_{int} = frac{lambda_{3333}}{4!}phi_3^4 + frac{lambda_{3111}}{3!}phi_3phi_1^3 + frac{lambda_{3221}}{2!}phi_3phi_2^2phi_1 + frac{lambda_{3211}}{2!}phi_3phi_2phi_1^2 + space…
$$
Now I need to calculate the invariant amplitude for the decay $phi_3rightarrowphi_2phi_1phi_1$ by applying Wick’s theorem and I only need to keep the dominant terms.

I already calculated it using the series expansion of the Dyson’s formula and by solving the integrals. But I think it is way faster using Wick’s theorem. (And I’m not sure if I’ve solved everything correctly either.) I would really appreciate some explanations or tips!