A company requires employees to create a $4$-digit passcode using the digits $0$ through $9$. The same digit can be repeated, and the digits must be entered in a specific order to unlock the system.

Is it appropriate to call this a 'combination' code? Why or why not?

A person is attempting to insert a key into a lock, but it is dark, and he cannot see the key or the lock. The key must be inserted with the correct side up ($2$ possibilities), and it must be inserted in the right orientation ($2$ possibilities) so that the teeth of the key align with the mechanism inside the lock. What is the probability of inserting the key correctly if he randomly selects an orientation for the key?

In a raffle game, each participant buys a $\$1$ ticket and chooses $4$ different numbers from $1$ to $60$, without replacement. To win, a participant must select the exact same $4$ numbers (order does not matter) that are drawn.

Given that there are $487,635$ possible combinations, what should the prize amount be to ensure an average profit of $50\%$, which is typical for raffles?

A tech company employs $120$ programmers: $80$ specialize in software and $40$ in hardware. The company wants to create a project team of $5$ programmers that represents both specialties. How should the company select a representative sample for the team?

A total of $40$ employees completed a workplace safety course. Their ratings are summarized below:

If three employees are selected randomly without replacement, what is the probability that all three received a rating of good or satisfactory?

Calculate the value of $\frac{{}^9{C}_5}{{}^{12}{C}_5}$.