Question Number 44237 by 12344 last updated on 24/Sep/18
$$\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{6}\:\mathrm{people}\:\mathrm{sit}\:\mathrm{around}\:\mathrm{a}\:\mathrm{roundtable}? \\ $$$$\mathrm{I}\:\mathrm{need}\:\mathrm{workings}\:\mathrm{please}? \\ $$
Answered by Hitarth Rana last updated on 24/Sep/18
$$\mathrm{5}!\:=\:\mathrm{120} \\ $$
Commented by Hitarth Rana last updated on 24/Sep/18
$${In}\:{this}\:{type}\:{of}\:{problem},\:{the}\:{answer}\:{is}\:\left({n}ā\mathrm{1}\right)! \\ $$
Answered by MrW3 last updated on 25/Sep/18
$${on}\:{a}\:{round}\:{table}\:{it}\:{doesnt}\:{mater}\:{who} \\ $$$${sits}\:{in}\:{which}\:{seat}.\:\:{assume}\:{there}\:{are} \\ $$$${one}\:{woman}\:{and}\:\mathrm{5}\:{men}.\:{the}\:{woman} \\ $$$${takes}\:{a}\:{place}\:{at}\:{first}.\: \\ $$$${we}\:{know}\:{to}\:{arrange}\:{the} \\ $$$${other}\:\mathrm{5}\:{persons}\:{there}\:{are}\:\mathrm{5}!\:{ways}. \\ $$$${therefore}\:{the}\:{answer}\:{is}\:\mathrm{5}!=\mathrm{120}. \\ $$