= Solution
For $\Psi(p_1)\to\chi(p_2)+\phi(k_1)+\phi(k_2)$, the sole <tree-level Feynman diagram> has a <Yukawa coupling> <interaction vertex> producing an off-shell <scalar field> particle of <four-momentum> $q=p_1-p_2=k_1+k_2$, followed by its cubic <scalar field> <interaction vertex>. Its invariant <decay amplitude> is
$$
\boxed{i\mathcal M=(-ig)(-i\lambda)\,
\bar u_\chi(p_2)u_\Psi(p_1)\,
\frac{i}{(k_1+k_2)^2-m^2+i0}.}
$$
Two successive <Yukawa coupling> <interaction vertices> would change the <fermion> species twice and leave a $\Psi$, so they cannot produce this final state. Interchanging the two identical outgoing <bosons> does not create another <Feynman diagram>; the cubic factorial is already included in the <Feynman rule>. The integrated <decay width> instead includes the <identical final-state symmetry factor> $1/2!$.
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