Think of the differences between circuit$-$switching and packet$-$switching paradigms in the Internet core design. Assume an Internet Service Provider $($ISP$)$ has an access link with $1$ Gbps capacity and, each user is active $5\%$ of the time. When active, a user generates data at a constant rate of $25$ Mbps$.$ Assume that there is a total of $80$ users subscribed to this ISP. Please answer the following questions. Show your work.

i$.$What is the maximum number of users the ISP can serve if it is implementing

a circuit$-$switching core?

ii$.$What is the probability that $1$ user will be active?

iii. What is the probability that more than $1$ users will be active?

iv$.$What is the probability that more than $2$ users will be active?

v$.$What is the probability the ISP will not be able to serve some of its users $($i$.$e$.,$ the amount of users$$ traffic exceeds the access link$$s capacity$)$ if it is implementing a packet$-$switching core? Use scientific notation to show your answer.