How many 5 letter passwords can be created using 3 A's and 2 B's? Order matters. Thanks for any help
S stop sine New member Joined Sep 9, 2008 Messages 1 Sep 9, 2008 #1 How many 5 letter passwords can be created using 3 A's and 2 B's? Order matters. Thanks for any help
D Denis Senior Member Joined Feb 17, 2004 Messages 1,707 Sep 9, 2008 #2 AAABB AABAB .... BBAAA kapish?
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 Sep 10, 2008 #3 Hello, stop sine! How many 5-letter passwords can be created using 3 A's and 2 B's? Order matters. Click to expand... There are 5 blanks to fill: _ _ _ _ _\displaystyle \text{There are 5 blanks to fill: }\;\_\;\_\;\_\;\_\;\_There are 5 blanks to fill: _____ Choose 3 of them for the A’s. There are: (53) = 5!3!2! = 10 ways.\displaystyle \text{Choose 3 of them for the A's. }\:\text{There are: }\:{5\choose3} \:=\:\frac{5!}{3!2!} \:=\:10\text{ ways.}Choose 3 of them for the A’s. There are: (35)=3!2!5!=10 ways. Then drop the 2 B’s in the remaining spaces.\displaystyle \text{Then drop the 2 B's in the remaining spaces.}Then drop the 2 B’s in the remaining spaces. . . Therefore, there are 10 possible passwords.\displaystyle \text{Therefore, there are }\boxed{10}\text{ possible passwords.}Therefore, there are 10 possible passwords.
Hello, stop sine! How many 5-letter passwords can be created using 3 A's and 2 B's? Order matters. Click to expand... There are 5 blanks to fill: _ _ _ _ _\displaystyle \text{There are 5 blanks to fill: }\;\_\;\_\;\_\;\_\;\_There are 5 blanks to fill: _____ Choose 3 of them for the A’s. There are: (53) = 5!3!2! = 10 ways.\displaystyle \text{Choose 3 of them for the A's. }\:\text{There are: }\:{5\choose3} \:=\:\frac{5!}{3!2!} \:=\:10\text{ ways.}Choose 3 of them for the A’s. There are: (35)=3!2!5!=10 ways. Then drop the 2 B’s in the remaining spaces.\displaystyle \text{Then drop the 2 B's in the remaining spaces.}Then drop the 2 B’s in the remaining spaces. . . Therefore, there are 10 possible passwords.\displaystyle \text{Therefore, there are }\boxed{10}\text{ possible passwords.}Therefore, there are 10 possible passwords.
