Question Number 220625 by Spillover last updated on 17/May/25
Answered by mr W last updated on 17/May/25
$${for}\:{the}\:{remaining}\:\mathrm{4}\:{doors}\:{he}\:{needs} \\ $$$${additional}\:{paint}\:{which}\:{can}\:{only}\:{be}\: \\ $$$${blue},\:{green}\:{or}\:{yellow}. \\ $$$$\left.\mathrm{1}\right)\:{color}\:{for}\:{addtional}\:{paint}\:{is}\:{blue} \\ $$$$\mathrm{5}\:{green}\:{doors},\:\mathrm{3}\:{yellow}\:{doors},\:\mathrm{4}\:{blue}\:{doors} \\ $$$$\frac{\mathrm{12}!}{\mathrm{5}!\mathrm{3}!\mathrm{4}!}=\mathrm{27720}\:{ways} \\ $$$$\left.\mathrm{2}\right)\:{color}\:{for}\:{addtional}\:{paint}\:{is}\:{green} \\ $$$$\mathrm{9}\:{green}\:{doors},\:\mathrm{3}\:{yellow}\:{doors} \\ $$$$\frac{\mathrm{12}!}{\mathrm{9}!\mathrm{3}!}=\mathrm{220}\:{ways} \\ $$$$\left.\mathrm{3}\right)\:{color}\:{for}\:{addtional}\:{paint}\:{is}\:{yellow} \\ $$$$\mathrm{5}\:{green}\:{doors},\:\mathrm{7}\:{yellow}\:{doors} \\ $$$$\frac{\mathrm{12}!}{\mathrm{5}!\mathrm{7}!}=\mathrm{792}\:{ways} \\ $$$$ \\ $$$${totally}:\:\mathrm{27720}+\mathrm{220}+\mathrm{792}=\mathrm{28732}\:{ways}\:\checkmark \\ $$
Commented by Spillover last updated on 17/May/25
$${correct} \\ $$