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In class I showed that the
probability that a random permutation
had at least one fixed point could be computed using the
Inclusion-Exclusion Principle for *n* events:

taking *E*_{i} the vent that the *i*th point is a fixed point.
We can see that
and that

As there are
pairs *i*<*j* and
triples *i*<*j*<*k* , the formula gives:

Note that this does not depend on *n*.

*Susan Holmes*

*1998-12-07*