Students are required to create $6-$character long passwords to access the library. The

letters must be from lowercase letters or digits. Each password must contain at most two

lowercase$-$letters and contains no repeated digits. The second letter must be always $"1"$

and the last letter always must be a digit. How many valid passwords are there? You are

required to show your work step$-$by$-$step. $[4$ marks$]$

Note:$1$h$032$a is invalid because the second letter is not $1\mathrm{.}314g05$ is valid because there is

one lower$-$case letter, no digits are repeated, the second letter is $1$ and the last letter is a

digit.Design a Finite State Automaton $($FSA$)$ that accepts binary numbers greater than $0,$ whose

decimal equivalents are divisible by $5.$ For instance, the FSA should accept inputs like

$\text{'}1010\text{'}($decimal equivalent: $10),$ and $\text{'}101\text{'}($decimal equivalent: $5),$ but it rejects inputs like

$\text{'}1101\text{'}($decimal equivalent: $13)$ and $\text{'}1001\text{'}($decimal equivalent: $9).[4$ marks$]$