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Question Number 167979 by nadovic last updated on 31/Mar/22
$$\mathrm{3}\:\mathrm{men}\:\mathrm{and}\:\mathrm{4}\:\mathrm{women}\:\mathrm{are}\:\mathrm{to}\:\mathrm{sit}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{table}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{possible}\:\mathrm{sitting}\:\mathrm{arrangements}\:\mathrm{if} \\ $$$$\:\left({a}\right)\:\mathrm{they}\:\mathrm{sit}\:\mathrm{in}\:\mathrm{a}\:\mathrm{row}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{men}\:\mathrm{must}\:\mathrm{not}\:\mathrm{sit}\:\mathrm{next}\:\mathrm{to}\:\mathrm{each} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{other}. \\ $$$$\:\left({b}\right)\:\mathrm{they}\:\mathrm{sit}\:\mathrm{in}\:\mathrm{circular}\:\mathrm{pattern}\:\mathrm{and} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{the}\:\mathrm{clockwise}\:\mathrm{and}\:\mathrm{anticlockwise} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{orders}\:\mathrm{are}\:\mathrm{considered}\:\mathrm{the}\:\mathrm{same}. \\ $$
Answered by mr W last updated on 31/Mar/22
$$\left({a}\right) \\ $$$$\square{W}\square{W}\square{W}\square{W}\square \\ $$$${C}_{\mathrm{5}} ^{\mathrm{3}} ×\mathrm{3}!×\mathrm{4}!=\mathrm{1440}\:{arrangements} \\ $$
Commented by mr W last updated on 31/Mar/22
$$\left({b}\right) \\ $$$$\frac{\left(\mathrm{7}−\mathrm{1}\right)!}{\mathrm{2}}=\mathrm{360} \\ $$
Commented by Tawa11 last updated on 01/Apr/22
$$\mathrm{Great}\:\mathrm{sir} \\ $$
Commented by peter frank last updated on 01/Apr/22
$$\mathrm{what}\:\mathrm{if}\:\mathrm{woman}\:\mathrm{must}\:\mathrm{not}\:\mathrm{seat}\:\mathrm{each} \\ $$$$\mathrm{other} \\ $$
Commented by mr W last updated on 01/Apr/22
$${WMWMWMW} \\ $$$$\mathrm{3}!×\mathrm{4}!=\mathrm{144}\:{arrangements} \\ $$