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Question Number 132854 by EDWIN88 last updated on 17/Feb/21
$$\mathrm{It}\:\mathrm{is}\:\mathrm{required}\:\mathrm{to}\:\mathrm{seat}\:\mathrm{5}\:\mathrm{men}\:\mathrm{and}\:\mathrm{4}\:\mathrm{women}\: \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{row}\:\mathrm{so}\:\mathrm{that}\:\mathrm{the}\:\mathrm{women}\:\mathrm{occupy}\:\mathrm{the}\:\mathrm{even}\: \\ $$$$\mathrm{place}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{such}\:\mathrm{arrangements}\:\mathrm{are} \\ $$$$\mathrm{possible}\:?\: \\ $$
Answered by bramlexs22 last updated on 17/Feb/21
$$\:=\:\mathrm{P}_{\mathrm{5}} ^{\mathrm{5}} \:×\:\mathrm{P}_{\mathrm{4}} ^{\mathrm{4}} \:=\:\mathrm{5}!×\mathrm{4}!\:=\:\mathrm{120}×\mathrm{24}=\mathrm{2880} \\ $$$$ \\ $$