A manufacturer from Syracuse produces motor boats, called $$Gliders$",$ sold as the top$-$rated small boats by the industry. Only a flawless perfect boat will be sold as a $$Glider$.$ Due to the company$$s inspection standard, its production site finds a boat has a $75\%$ probability to be perfect for being badged as a $$Glider$$ and a $25\%$ probability to be defective. The perfect $$Glider$$ boats are highly praised by the industry testing groups and sold with a unit profit of $$9,000$ per boat. A defective boat is initially inspected and later repaired to be sold as a $$Refurbished$$ boat with a unit profit of $$3,000$ per boat. In December $2023,$ a batch of $12$ boats from this production line is collected.

$($Question B$-1)$ What is the probability that exactly $11$ boats from this December $2023$ batch are perfect and badged as $$Gliders$?$

$($Question B$-2)$ What is the probability that there are no more than $2$ defective boats from this December $2023$ batch?

$($Question B$-3)$ What is the probability that this December $2023$ batch can bring in a total profit of more than $$88,000?$