Using proton-proton collision data, corresponding to an integrated luminosity
of 9fb−1 collected with the LHCb detector, seven decay modes of the
Bc+ meson into a J/ψ or ψ(2S) meson and three charged hadrons,
kaons or pions, are studied. The decays Bc+→(ψ(2S)→J/ψπ+π−)π+, Bc+→ψ(2S)π+π+π−, Bc+→J/ψK+π+π− and
Bc+→K+K+K− are observed for the first time, and evidence for
the Bc+→ψ(2S)K+K−π+ decay is found, where J/ψ and
ψ(2S) mesons are reconstructed in their dimuon decay modes. The ratios of
branching fractions between the different Bc+ decays are reported as well
as the fractions of the decays proceeding via intermediate resonances. The
results largely support the factorisation approach used for a theoretical
description of the studied decays