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Question Number 133316 by bramlexs22 last updated on 21/Feb/21
$$\mathrm{How}\:\mathrm{many}\:\mathrm{6}−\mathrm{letter}\:\mathrm{words}\:\mathrm{in}\: \\ $$$$\mathrm{which}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{letter}\:\mathrm{appears} \\ $$$$\mathrm{more}\:\mathrm{than}\:\mathrm{once}\:,\mathrm{can}\:\mathrm{be}\:\mathrm{made}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{letters}\:\mathrm{in}\:\mathrm{the}\:\mathrm{word}\:\mathrm{FLIGHT} \\ $$$$ \\ $$
Commented by mr W last updated on 21/Feb/21
$$\mathrm{6}^{\mathrm{6}} −\mathrm{6}!=\mathrm{45936} \\ $$
Answered by EDWIN88 last updated on 21/Feb/21
$$=\:\mathrm{6}^{\mathrm{6}} −\mathrm{720}\:=\:\mathrm{45}\:\mathrm{936} \\ $$$$ \\ $$
Answered by mr W last updated on 22/Feb/21
$${an}\:{other}\:{way}: \\ $$$${words}\:{with}\:{one}\:{letter}:\:{C}_{\mathrm{1}} ^{\mathrm{6}} ×\mathrm{1}=\mathrm{6} \\ $$$${words}\:{with}\:{two}\:{letters}:\:{C}_{\mathrm{2}} ^{\mathrm{6}} ×\mathrm{62}=\mathrm{930} \\ $$$${words}\:{with}\:{three}\:{letters}:\:{C}_{\mathrm{3}} ^{\mathrm{6}} ×\mathrm{540}=\mathrm{10800} \\ $$$${words}\:{with}\:{four}\:{letters}:\:{C}_{\mathrm{4}} ^{\mathrm{6}} ×\mathrm{1560}=\mathrm{23400} \\ $$$${words}\:{with}\:{five}\:{letters}:\:{C}_{\mathrm{5}} ^{\mathrm{6}} ×\mathrm{1800}=\mathrm{10800} \\ $$$$\Sigma=\mathrm{45936} \\ $$