5. (16 pts) For the following problem, ignore the year of birth while comparing two birthdays. Moreover, assume that the year is exactly 365 days (ignore the 29th of February). Note that matching birthdays means the birthdays are the same. (a) (4 pts) You are a member of a class room that has n 1 students including you. What is the probability that you find at least one student, other than you, who has a birthday that matches yours

Brittany has designed four different birdcages, each with the same volume: a square pyramid, a cylinder, a cone, and a sphere. the zoo wants to use one of brittany’s designs but plans to change the volume of the cage. find the design change that would result in the birdcage with the greatest volume. a.) increase the area of the base of the square pyramid by a factor of ten. b.) increase the height of the cylinder by a factor of ten. c.) increase the radius of the cone by a factor of ten. d.) increase the radius of a sphere by a factor of ten.