Question

You need to have a password with six letters followed by three odd digits between zero and nine,inclusive, if the characters and digits cannot be used more than once how many choices do you have for your password

Answer 1

`9,945,936,000`

1) Since there are 26 letters from A to Z and 5 odd digits from 0 to 9. And no repetition was allowed, we can solve this problem by doing the following:

2) Note that the numbers represent the possibilities. Now, let's multiply all that:

`\begin{gathered} _(26)P_6*_5P_3= \\ \\ (26!)/((26-6)!)*(5!)/((5-3)!) \\ \\ (26!)/(20!)*(5!)/(2!) \\ \\ (26*25*24*23*22*21*20!)/(20!)*(5*4*3*2!)/(2!) \\ \\ (26*\:25*\:24*\:23*\:22*\:21)*(5*4*3) \\ \\ 9,945,936,000 \end{gathered}`

Thus, this is the number of possible passwords.