Question Number 56615 by pieroo last updated on 19/Mar/19
$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{different}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{the} \\ $$$$\mathrm{letters}\:\mathrm{of}\:\mathrm{the}\:\mathrm{word}\:\mathrm{OKINKWO}\:\mathrm{be}\:\mathrm{arranged}?\: \\ $$$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{of}\:\mathrm{these}\:\mathrm{arrangements} \\ $$$$\mathrm{does}\:\mathrm{an}\:\mathrm{O}\:\mathrm{occupy}\:\mathrm{both}\:\mathrm{end}\:\mathrm{points}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{word}? \\ $$
Commented by mr W last updated on 19/Mar/19
$$\left(\mathrm{1}\right)\:\frac{\mathrm{7}!}{\mathrm{2}!\mathrm{2}!}=\mathrm{1260} \\ $$$$\left(\mathrm{2}\right)\:\frac{\mathrm{5}!}{\mathrm{2}!}=\mathrm{60} \\ $$
Commented by pieroo last updated on 19/Mar/19
$$\mathrm{thank}\:\mathrm{sir}.\:\mathrm{please}\:\mathrm{do}\:\mathrm{share}\:\mathrm{some}\:\mathrm{lights} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{second}\:\mathrm{one}\:\mathrm{for}\:\mathrm{me}. \\ $$
Commented by Joel578 last updated on 19/Mar/19
$${O}\:\_\:\_\:\_\:\_\:\_\:{O} \\ $$$$\mathrm{that}\:\mathrm{means}\:\mathrm{we}\:\mathrm{only}\:\mathrm{have}\:\mathrm{to}\:\mathrm{arrange}\:{K},\:{I},\:{N},\:{K},\:{W} \\ $$$$\mathrm{arrange}\:\mathrm{5}\:\mathrm{letters}\:=\:\mathrm{5}! \\ $$$$\mathrm{but}\:\mathrm{there}\:\mathrm{is}\:\mathrm{2}\:{K}'\mathrm{s},\:\mathrm{so}\:\mathrm{we}\:\mathrm{divide}\:\mathrm{it}\:\mathrm{by}\:\mathrm{2}! \\ $$$$\Rightarrow\:\frac{\mathrm{5}!}{\mathrm{2}!} \\ $$
Commented by pieroo last updated on 19/Mar/19
$$\mathrm{Ok}\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}. \\ $$