A password for a computer system requires exactly $6$ characters. Each character can be either one of the $26$ letters from A to Z or one of the ten digits from $0$ to $9$. The first character must be a letter and the last character must be a digit. How many different possible passwords are there?

The password required has to be of 6 characters and the first of those should be one of the 26 letters, the last must be one of the 10 digits and the remaining four can be either of those 36.

Thus, the possibilities for first place become 26, for the next four places become 36, and for the last place become 10.

The total number of possibilities therefore become $36 \times (26)^4 \times 10 = 16,45,11,360$

This can be written as $1.6451136 \times 10^8$ and thus lies between $10^8$ and $10^9$