Coding

In order to enter the database and update their information, the agents need to choose a password. A password should look like this:

$$ Exactly $3$ a$.$

$$ At least $2$ c$.$

$$ Any number of b$\text{'}$s$.$

The characters may appear in any order, as long as they are sufficiently numerous.

To check whether a string from the alphabet $\{$ a$,$ b$,$ c $\}$ is a permitted password, an accepting machine is needed.

$4.$ Analyze with the help of combinatorics how many states the automaton needs to have.

$5.$ Draw an accepting automaton that recognizes the language of allowed passwords. Explain

also what each of the conditions entails.

$6.$ Write a regular expression for the language. Explain carefully how you reason.