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{\bf John D. Dixon }
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{\bf Asymptotics of Generating the Symmetric and Alternating Groups}
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The probability that a random pair of elements from the alternating
group $A_{n}$ generates all of $A_{n}$ is shown to have an asymptotic
expansion of the form
$1-1/n-1/n^{2}-4/n^{3}-23/n^{4}-171/n^{5}-...~$. \ This same
asymptotic expansion is valid for the probability that a random pair
of elements from the symmetric group $S_{n}$ generates either $A_{n}$
or $S_{n}$. Similar results hold for the case of $r$ generators
($r>2$).

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