MathDB

Among citizens of Cambridge there exist

8

different types of blood antigens. In a crowded lecture hall are

256

students, each of whom has a blood type corresponding to a distinct subset of the antigens; the remaining of the antigens are foreign to them.
Quito the Mosquito flies around the lecture hall, picks a subset of the students uniformly at random, and bites the chosen students in a random order. After biting a student, Quito stores a bit of any antigens that student had. A student bitten while Quito had

k

blood antigen foreign to him/her will suffer for

k

hours. What is the expected total suffering of all

256

students, in hours?

Problem Statement