A truck rental company has a fleet of $5$ trucks. It rents them out at RM$80$ per truck per day.

The daily demand for trucks is known to follow a Poisson distribution with mean $5.$

$($i$)$ Calculate the probability that the demand for trucks on a particular day can be met.

$($ii$)$ Demonstrate the probability distribution for the daily income received from the truck

rental.

$($iii$)$ Examine the expected daily income received from the rental.