Probability can be approximately understood as a relative proportion [similar to percentages J but scaled to 1} instead of an exact number For example in a given university class assume that 15f30th of the class has to more than 120 {assumed intelligent LTN'BDth of the class likes chocolate ,and Sfath of the class likes statistics a. What is an upper bound on the probability that a randomly sampled student will like either chocolate or statistics ? b. if the probability of the students Fiking both chocolate and statistics is 5f30,what is the probability of students liking either chocolate or statistics ? c. if we additionally know that only intelligent students no greater than IZDllike chocolate or statistics , what is the probability of students being not intelligent in the class ? Monash University uses Allocate +to allocate tutoriai [laboratory sessions to students ,one allocation for each student .Assume there are 400 students enrolled for ENGSDGI and that the allocation is random instead of preference based . Note :none of the below numbers need to be simplified to a single number i. Suppose there are only 2 labs available and that there is no limit to the number of students that can be assigned to either lab. How many different possible combinations of students can there be?what is the number if there were 10 labs ? Note that each student gets only one allocation ii. Say instructor only wants to know the number of students enrolled in each of the two sessions and doesn't care about which particular students are in each .How many possible class sizes could you see for the two tutorials ? iii. Assume that the size of one of the labs is fixed to exactly 5 students, with 5 seats arranged ,and that all students are present .Assume a seating arrangement is different even if one student is different or differently seated .How many possible seating arrangements can there be using the 400 students ? iv. Now consider that the seating arrangement is not important and only students in the class are of interest .Assume that a lab is different even if a single student changes . How many different labs can the tutor see ? v. Finally ,consider that there are now 10 labs running with exactly 40 students in each lab. Assuming we don't care about the arrangement of students within a lab, howI many different unique combinations of students and labs are possible