How is the counting principle mathematically used?

Need this asap if anyone can i would be very grateful. if you could show workings that would really

You got a job selling magazines door-to-door. you are paid $100 per day plus $1.50 for each magazine you sell. which recursive formula models this situation?

Parabolas y=−2x^2 and y=2x^2 +k intersect at points a and b that are in the third and the fourth quadrants respectively. find k if length of the segment ab is 5.