  We present a simple randomized polynomial time algorithm to approximate the
mixed discriminant of $n$ positive semidefinite $n \times n$ matrices within a
factor $2^{O(n)}$. Consequently, the algorithm allows us to approximate in
randomized polynomial time the permanent of a given $n \times n$ non-negative
matrix within a factor $2^{O(n)}$. When applied to approximating the permanent,
the algorithm turns out to be a simple modification of the well-known
Godsil-Gutman estimator.
