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Question Number 103367 by bobhans last updated on 14/Jul/20
$${many}\:{words}\:{with}\:\mathrm{4}\:{letters}\:{can}\:{be}\:{formed} \\ $$$${using}\:{letters}\:{from}\:{the}\:{word} \\ $$$${TINKUTARA}\:{is}\:\_\_\_ \\ $$
Answered by mr W last updated on 15/Jul/20
$${we}\:{have}\:{following}\:{letters}: \\ $$$${AA},{TT},{INKUR} \\ $$$$ \\ $$$${to}\:{form}\:{a}\:\mathrm{4}\:{letter}\:{word},\:{we}\:{have} \\ $$$${following}\:{cases}: \\ $$$${xxyy}\:\Rightarrow\frac{\mathrm{4}!}{\mathrm{2}!\mathrm{2}!}=\mathrm{6}\:{ways} \\ $$$${xxyz}\:\Rightarrow\mathrm{2}×{C}_{\mathrm{2}} ^{\mathrm{6}} ×\frac{\mathrm{4}!}{\mathrm{2}!}=\mathrm{360}\:{ways} \\ $$$${xyzw}\:\Rightarrow{C}_{\mathrm{4}} ^{\mathrm{7}} ×\mathrm{4}!=\mathrm{840}\:{ways} \\ $$$$\Rightarrow{total}\:\mathrm{6}+\mathrm{360}+\mathrm{840}=\mathrm{1206} \\ $$
Commented by bramlex last updated on 15/Jul/20
$$\mathrm{cooll} \\ $$