A professor asks n students to peer grade their test papers. He hands out one of…

A professor asks n students to peer grade their test papers. He
hands out one of the n papers to each student uniformly at random.
Show that with probability at least at 1−1/k, not more than k
students get their own test paper. Hint: Consider the random
variable Xi that denotes whether student i gets his/her own paper.
Use Markov’s inequality.

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