Handing back tests

A professor randomly hands back test in a class of \(n\) people paying no attention to the names on the paper. Let \(N\) denote the number of people who got the right test. Let \(D\) denote the pairs of people who got each others tests. Let \(T\) denote the number of groups of three who none got the right test but yet among the three of them that have each others tests. Find:

  1. \(\mathbf{E} (N)\)
  2. \(\mathbf{E} (D)\)
  3. \(\mathbf{E} (T)\)

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