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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

$$\left(1\right)\frac{7!}{2!2!}=1260$$$$\left(2\right)\frac{5!}{2!}=60$$

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

$$O\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}O$$$$\mathrm{that}\mathrm{means}\mathrm{we}\mathrm{only}\mathrm{have}\mathrm{to}\mathrm{arrange}K,I,N,K,W$$$$\mathrm{arrange}5\mathrm{letters}=5!$$$$\mathrm{but}\mathrm{there}\mathrm{is}2K^{\prime }\mathrm{s},\mathrm{so}\mathrm{we}\mathrm{divide}\mathrm{it}\mathrm{by}2!$$$$\Rightarrow \frac{5!}{2!}$$

Commented by pieroo last updated on 19/Mar/19

$$\mathrm{Ok}\mathrm{God}\mathrm{bless}\mathrm{you}.$$

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