Question-220626

Question Number 220626 by Spillover last updated on 17/May/25

Answered by mr W last updated on 17/May/25

1) 4 couples in one compartment ⇒2 ways 2) 3 couples in one compartment 2×C_4 ^3 ×C_8 ^2 =224 ways 2) 2 couples in each compartment C_4 ^2 ×C_8 ^4 =420 ways totally: 2+224+420=646 ways ✓

$$\left.\mathrm{1}\right)\:\mathrm{4}\:{couples}\:{in}\:{one}\:{compartment} \\ $$$$\Rightarrow\mathrm{2}\:{ways} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{3}\:{couples}\:{in}\:{one}\:{compartment} \\ $$$$\mathrm{2}×{C}_{\mathrm{4}} ^{\mathrm{3}} ×{C}_{\mathrm{8}} ^{\mathrm{2}} =\mathrm{224}\:{ways} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{2}\:{couples}\:{in}\:{each}\:{compartment} \\ $$$${C}_{\mathrm{4}} ^{\mathrm{2}} ×{C}_{\mathrm{8}} ^{\mathrm{4}} =\mathrm{420}\:{ways} \\ $$$$ \\ $$$${totally}:\:\mathrm{2}+\mathrm{224}+\mathrm{420}=\mathrm{646}\:{ways}\:\checkmark \\ $$

Commented by Spillover last updated on 17/May/25