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Question Number 133314 by bramlexs22 last updated on 21/Feb/21
$$\mathrm{How}\:\mathrm{many}\:\mathrm{rearrangements}\:\mathrm{are}\: \\ $$$$\mathrm{there}\:\mathrm{of}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{in}\:\mathrm{the}\:\mathrm{world} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{ENGINEERING} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{MATHEMATICAL}\: \\ $$
Answered by EDWIN88 last updated on 21/Feb/21
$$\left(\mathrm{i}\right)\:=\frac{\mathrm{11}!}{\mathrm{3}!\mathrm{3}!\mathrm{2}!\mathrm{2}!}\:=\:\mathrm{277200} \\ $$$$\left(\mathrm{ii}\right)=\frac{\mathrm{12}!}{\mathrm{2}!\mathrm{3}!\mathrm{2}!}=\mathrm{1}.\mathrm{99584E7}=\mathrm{19}\:\mathrm{958}\:\mathrm{400}\: \\ $$