Question Number 133995 by mr W last updated on 26/Feb/21
![in how many ways can n men and n women be arranged in a row such that men and women alternate?](https://www.tinkutara.com/question/Q133995.png)
$${in}\:{how}\:{many}\:{ways}\:{can}\:{n}\:{men}\:{and} \\ $$$${n}\:{women}\:{be}\:{arranged}\:{in}\:{a}\:{row}\:{such} \\ $$$${that}\:{men}\:{and}\:{women}\:{alternate}? \\ $$
Commented by benjo_mathlover last updated on 26/Feb/21
![= 2×n!×n! = 2×(n!)^2 example { ((3 women)),((3 men)) :} MWMWMW = 3!×3! WMWMWM=3!×3! totally = 2×3!×3!](https://www.tinkutara.com/question/Q134001.png)
$$=\:\mathrm{2}×\mathrm{n}!×\mathrm{n}!\:=\:\mathrm{2}×\left(\mathrm{n}!\right)^{\mathrm{2}} \\ $$$$\mathrm{example}\:\begin{cases}{\mathrm{3}\:\mathrm{women}}\\{\mathrm{3}\:\mathrm{men}}\end{cases} \\ $$$$\:\mathrm{MWMWMW}\:=\:\mathrm{3}!×\mathrm{3}! \\ $$$$\mathrm{WMWMWM}=\mathrm{3}!×\mathrm{3}! \\ $$$$\mathrm{totally}\:=\:\mathrm{2}×\mathrm{3}!×\mathrm{3}! \\ $$
Commented by mr W last updated on 26/Feb/21
![thanks!](https://www.tinkutara.com/question/Q134004.png)
$${thanks}! \\ $$