Question Number 224634 by gregori last updated on 23/Sep/25
$$\:\:\underbrace{\mathcal{X}} \\ $$
Answered by mr W last updated on 24/Sep/25
$$\_{B\_B\_B\_B\_B\_B\_G\_G\_G\_G\_} \\ $$$$\_{G\_G\_G\_G\_B\_B\_B\_B\_B\_B\_} \\ $$$${B}\ast{B}\ast{B}\ast{B}\ast{B}\ast{B} \\ $$$${G}\lozenge{G}\lozenge{G}\lozenge{G} \\ $$$$\_\:{means}\:{empty}\:{chair}\:\left({E}\right) \\ $$$$\ast\:{means}\:{EGGGG}\:{or}\:{GGGGE} \\ $$$$\lozenge\:{means}\:{EBBBBBB}\:{or}\:{BBBBBBE} \\ $$$${answer}: \\ $$$$\:\mathrm{2}×\mathrm{6}!×\mathrm{4}!×\mathrm{11}+\mathrm{6}!×\mathrm{5}×\mathrm{2}×\mathrm{4}!+\mathrm{4}!×\mathrm{3}×\mathrm{2}×\mathrm{6}! \\ $$$$=\mathrm{656}\:\mathrm{640}\:\checkmark \\ $$