Let $S_k=3^k{}^{100}{C}_0{}^{100}{C}_k-3^{k-1}{}^{100}{C}_1{}^{99}{C}_{k-1}+3^{k-2}{}^{100}{C}_2{}^{98}{C}_{k-2}+\mathrm{...}+{\left(-1\right)}^k{}^{100}{C}_k{}^{100-k}{C}_0,$
  then select correct alternative(s) $\left(k=0,1,2,\mathrm{.....},100\right)$

$S_1+S_3+S_5+\mathrm{....}+S_{99}>S_2+S_4+\mathrm{....}+S_{100}$

$S_{67}$ is the greatest amongst these 101 numbers

 $S_{66}$ is the greatest amongst these 101 numbers

$S_1+S_3+S_5+\mathrm{....}+S_{99}\le S_2+S_4+\mathrm{....}+S_{100}$