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Question Number 153714 by pete last updated on 09/Sep/21
$$\mathrm{How}\:\mathrm{many}\:\mathrm{three}−\mathrm{digit}\:\mathrm{numbers}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{formed}\:\mathrm{using}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{2},\mathrm{3},\mathrm{5},\mathrm{7},\mathrm{8}\:\mathrm{if}\: \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{odd}\:\mathrm{and}\:\mathrm{no}\:\mathrm{digit}\:\mathrm{is}\:\mathrm{repeted}? \\ $$
Answered by EDWIN88 last updated on 09/Sep/21
$$=\:{P}_{\mathrm{1}} ^{\:\mathrm{3}} ×{P}_{\mathrm{2}} ^{\:\mathrm{4}} \:=\frac{\mathrm{3}!}{\mathrm{2}!}×\frac{\mathrm{4}!}{\mathrm{2}!}\:=\:\mathrm{6}×\mathrm{6}=\mathrm{36} \\ $$
Answered by puissant last updated on 09/Sep/21
$${A}_{\mathrm{3}} ^{\mathrm{1}} ×{A}_{\mathrm{4}} ^{\mathrm{2}} =\frac{\mathrm{3}!}{\left(\mathrm{3}−\mathrm{1}\right)!}×\frac{\mathrm{4}!}{\left(\mathrm{4}−\mathrm{2}\right)!} \\ $$$$=\mathrm{3}×\mathrm{4}×\mathrm{3} \\ $$$$=\mathrm{36}.. \\ $$