  We report, for the first time, the detection of the Mn-K$\alpha$ line in the
Type IIb supernova (SN IIb) remnant, Cassiopeia A. Manganese ($^{55}$Mn after
decay of $^{55}$Co), a neutron-rich element, together with chromium ($^{52}$Cr
after decay of $^{52}$Fe), is mainly synthesized at the explosive incomplete Si
burning regime. Therefore, the Mn/Cr mass ratio with its neutron excess
reflects the neutronization at the relevant burning layer during the explosion.
Chandra's archival X-ray data of Cassiopeia A indicate a low Mn/Cr mass ratio
with values in the range 0.10--0.66, which, when compared to one-dimensional SN
explosion models, requires that the electron fraction be 0.4990 $\lesssim
Y_{\rm e} \lesssim$ 0.5 at the incomplete Si burning layer. An explosion model
assuming a solar-metallicity progenitor with a typical explosion energy ($1
\times 10^{51}$ erg) fails to reproduce such a high electron fraction. In such
models, the explosive Si-burning regime extends only to the Si/O layer
established during the progenitor's hydrostatic evolution; the $Y_e$ in the
Si/O layer is lower than the value required by our observational constraints.
We can satisfy the observed Mn/Cr mass ratio if the explosive Si-burning regime
were to extend into the O/Ne hydrostatic layer, which has a higher $Y_{\rm e}$.
This would require an energetic ($> 2 \times 10^{51}$ erg) and/or asymmetric
explosion of a sub-solar metallicity progenitor ($Z \lesssim 0.5Z_{\odot}$) for
Cassiopeia A. The low initial metallicity can be used to rule out a single-star
progenitor, leaving the possibility of a binary progenitor with a compact
companion (white dwarf, neutron star or black hole). We discuss the
detectability of X-rays from Bondi accretion onto such a compact companion
around the explosion site. We also discuss other possible mass-loss scenarios
for the progenitor system of Cassiopeia A.
