$4.$ Shuffling Students

Suppose Professor Grumpy wants to shuffle the seating of

students in their Algorithms class $($who can understand why Prof G does what they do$).$ They have a $$uniform$$ shuffling algorithm which assigns each student to a given seat with probability

$.$ Use linearity of expectation $($C$\mathrm{.}24$ in Cormen$)$ to calculate the expected number of students who get to stay in their current seat.