2023 DHS P2 Q6

A student needs to create a \(7\)-character alpha-numeric passcode (that is, at least one letter and one digit must be included). She uses lower case letters from her name “venessa see” and digits \(1\) to \(9\).

1. Find the number of different passcodes if all the letters and numbers are distinct such that
   1. they begin with a letter and end with a digit,[2]
   2. all the letters and digits are to be separated.[3]
2. Find the number of different passcodes if there are \(3\) identical letters, and all other letters and digits are distinct.[3]