Question Number 124149 by I want to learn more last updated on 01/Dec/20
$$\mathrm{Two}\:\mathrm{men}\:\mathrm{and}\:\mathrm{four}\:\mathrm{women}\:\mathrm{line}\:\mathrm{up}\:\mathrm{at}\:\mathrm{a}\:\mathrm{checkout}\:\mathrm{counter}\:\mathrm{in}\:\mathrm{a}\:\mathrm{store}. \\ $$$$\left(\mathrm{a}\right)\:\:\:\:\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{they}\:\mathrm{line}\:\mathrm{up}??? \\ $$$$\left(\mathrm{b}\right)\:\:\:\:\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{they}\:\mathrm{line}\:\mathrm{up}\:\mathrm{if}\:\mathrm{the}\:\mathrm{first}\:\mathrm{person}\:\mathrm{line}\:\mathrm{is} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{a}\:\mathrm{woman}\:\mathrm{and}\:\mathrm{the}\:\mathrm{line}\:\mathrm{changes}\:\mathrm{by}\:\mathrm{gender}.\:\left(\mathrm{w},\:\:\mathrm{m},\:\:\mathrm{w},\:\:\mathrm{w},\:\:\mathrm{m},\:\:\mathrm{w}\right)?? \\ $$
Commented by I want to learn more last updated on 01/Dec/20
$$\left(\mathrm{a}\right)\:\:\:\:\mathrm{7}! \\ $$
Commented by I want to learn more last updated on 01/Dec/20
$$\mathrm{The}\:\:\mathrm{b}\:\:\mathrm{part}\:\mathrm{is}\:\mathrm{my}\:\mathrm{concern}. \\ $$
Commented by mr W last updated on 01/Dec/20
$${try}\:{to}\:{solve}\:{by}\:{yourself}\:{sir},\:{it}'{s}\:{not}\:{so} \\ $$$${hard}. \\ $$
Commented by I want to learn more last updated on 01/Dec/20
$$\mathrm{But}\:\mathrm{the}\:\left(\mathrm{b}\right),\:\mathrm{i}\:\mathrm{don}'\mathrm{t}\:\mathrm{understand}. \\ $$
Answered by mr W last updated on 01/Dec/20
$$\left({a}\right) \\ $$$$\mathrm{6}!=\mathrm{720} \\ $$$$\left({b}\right) \\ $$$${WMWWMW} \\ $$$$\mathrm{2}!\mathrm{4}!=\mathrm{48} \\ $$
Commented by I want to learn more last updated on 01/Dec/20
$$\mathrm{Thanks}\:\mathrm{sir}.\:\mathrm{I}\:\mathrm{appreciate}. \\ $$