  We perform a numerical simulation of a three-band Hubbard model with two
CuO$_2$ planes and a single CuO chain layer for YBCO cuprates. The
spin-fluctuation mediated pairing interaction is computed within the multiband
random-phase approximation, and its pairing eigenvalues and eigenfunctions are
solved as a function of chain state filling factor $n_c$. We find that for the
intrinsic value of $n_c$ in YBCO samples, one obtains the usual $d$-wave
pairing symmetry. However, if we dope the chain layers with holes, while
keeping the plane states doping fixed, the leading pairing symmetry solution
becomes an unconventional $f$-wave symmetry. The mechanism behind the $f$-wave
pairing is the competition between the plane states antiferromagnetic nesting
and chain states' uniaxial nesting. We also find that the pairing strength is
strongly augmented when the flat band bottom of the chain state passes the
Fermi level for a fixed plane states doping. The $f$-wave pairing symmetry can
be realized in YBCO cuprates in future experiments where the self-doping
mechanism between the chain and plane states can be minimized so that only
chain state can be selectively hole doped.
