= Solution
Choose the <charge conjugation> matrix so that $C^T=-C$ and $(\gamma^m)^T=-C\gamma^mC^{-1}$, and write $\bar\lambda=\lambda^TC$. Since the components are odd <Grassmann variables>,
$$
\lambda^TM\lambda=\frac12\lambda^T(M-M^T)\lambda.
$$
Thus a <symmetric matrix> gives zero, whereas a nonzero <antisymmetric matrix> can give a nonzero bilinear. The <four-dimensional Majorana bilinear vanishing criterion> follows by transposing an antisymmetrized product and reversing its $n$ factors:
$$
\bigl(C\gamma^{m_1\ldots m_n}\bigr)^T
=-(-1)^{n(n+1)/2}C\gamma^{m_1\ldots m_n}.
$$
For $n=0,1,2,3$, the symmetry types are respectively antisymmetric, symmetric, symmetric and antisymmetric. These are the same-spinor selection rules of the <Majorana spinor>; they would be reversed for a commuting spinor. \b[The vanishing choices are (a) and (c).]
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