Question Number 130685 by EDWIN88 last updated on 28/Jan/21
![How many password containing 6 characters of the letters in the word ′′ Move Now ′′ ?](https://www.tinkutara.com/question/Q130685.png)
$${How}\:{many}\:{password}\:{containing} \\ $$$$\mathrm{6}\:{characters}\:{of}\:{the}\:{letters}\:{in}\:{the}\: \\ $$$${word}\:''\:{Move}\:{Now}\:''\:? \\ $$
Answered by liberty last updated on 28/Jan/21
![case(1) O_− _− _− _− _(−−) = 6! case(2) O_− O_− _− _− _− _− = C_( 4) ^( 5) × ((6!)/(2!)) = 5×((6!)/2) totally many password is 6! + (5/2)×6! = 6! ((7/2))= 2520](https://www.tinkutara.com/question/Q130687.png)
$$\mathrm{case}\left(\mathrm{1}\right)\:\underset{−} {\mathrm{O}}\underset{−} {\:}\underset{−} {\:}\underset{−} {\:}\underset{−−} {\:}\:=\:\mathrm{6}! \\ $$$$\mathrm{case}\left(\mathrm{2}\right)\:\underset{−} {\mathrm{O}}\:\underset{−} {\mathrm{O}}\underset{−} {\:}\underset{−} {\:}\underset{−} {\:}\underset{−} {\:}\:=\:\mathrm{C}_{\:\mathrm{4}} ^{\:\mathrm{5}} \:×\:\frac{\mathrm{6}!}{\mathrm{2}!}\:=\:\mathrm{5}×\frac{\mathrm{6}!}{\mathrm{2}} \\ $$$$\mathrm{totally}\:\mathrm{many}\:\mathrm{password}\:\mathrm{is}\:\mathrm{6}!\:+\:\frac{\mathrm{5}}{\mathrm{2}}×\mathrm{6}! \\ $$$$=\:\mathrm{6}!\:\left(\frac{\mathrm{7}}{\mathrm{2}}\right)=\:\mathrm{2520} \\ $$
Answered by JDamian last updated on 28/Jan/21
![Permutations with repetition ((7!)/(2!))=((7!)/2)](https://www.tinkutara.com/question/Q130721.png)
$${Permutations}\:{with}\:{repetition} \\ $$$$ \\ $$$$\frac{\mathrm{7}!}{\mathrm{2}!}=\frac{\mathrm{7}!}{\mathrm{2}} \\ $$