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Question Number 51286 by aseerimad last updated on 25/Dec/18
Answered by mr W last updated on 26/Dec/18
$${Type}\:\mathrm{1}: \\ $$$${Number}\:{of}\:{words}\:{starting}\:{with}\:{D}: \\ $$$$=\frac{\mathrm{7}!}{\mathrm{2}!}=\mathrm{2520} \\ $$$$ \\ $$$${Type}\:\mathrm{2}: \\ $$$${Number}\:{of}\:{words}\:{ending}\:{with}\:{R}: \\ $$$$=\frac{\mathrm{2}!\mathrm{7}!}{\mathrm{2}!}=\mathrm{5040} \\ $$$${but}\:{in}\:{this}\:{number}\:{some}\:{words}\:{start} \\ $$$${with}\:{D}\:{which}\:{are}\:{already}\:{counted}\:{in} \\ $$$${type}\:\mathrm{1}. \\ $$$$ \\ $$$${Type}\:\mathrm{3}: \\ $$$${Number}\:{of}\:{words}\:{ending}\:{with}\:{R}\:{but} \\ $$$${starting}\:{with}\:{D}: \\ $$$$=\frac{\mathrm{2}!\mathrm{6}!}{\mathrm{2}!}=\mathrm{720} \\ $$$$ \\ $$$$\Rightarrow{result}\:{is}\:\mathrm{2520}+\mathrm{5040}−\mathrm{720}=\mathrm{6840} \\ $$
Commented by Tawa1 last updated on 26/Dec/18
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir},\:\mathrm{i}\:\mathrm{learn}\:\mathrm{more} \\ $$
Commented by aseerimad last updated on 26/Dec/18
$${thankyou}\:{sir}. \\ $$