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Martin Sleziak
Martin Sleziak
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In finite simple groups, most pairs of elements generate, so (at least asymptotically), the number of generating pairs is $\asymp |G|^2.$ See, for example:

Robert M. Guralnick, Martin W. Liebeck, Jan Saxl, and Aner Shalev, MR 1707675 Random generation of finite simple groupsRandom generation of finite simple groups, J. Algebra 219 (1999), no. 1, 345--355.

In finite simple groups, most pairs of elements generate, so (at least asymptotically), the number of generating pairs is $\asymp |G|^2.$ See, for example:

Robert M. Guralnick, Martin W. Liebeck, Jan Saxl, and Aner Shalev, MR 1707675 Random generation of finite simple groups, J. Algebra 219 (1999), no. 1, 345--355.

In finite simple groups, most pairs of elements generate, so (at least asymptotically), the number of generating pairs is $\asymp |G|^2.$ See, for example:

Robert M. Guralnick, Martin W. Liebeck, Jan Saxl, and Aner Shalev, MR 1707675 Random generation of finite simple groups, J. Algebra 219 (1999), no. 1, 345--355.

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Igor Rivin
Igor Rivin
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In finite simple groups, most pairs of elements generate, so (at least asymptotically), the number of generating pairs is $\asymp |G|^2.$ See, for example:

Robert M. Guralnick, Martin W. Liebeck, Jan Saxl, and Aner Shalev, MR 1707675 Random generation of finite simple groups, J. Algebra 219 (1999), no. 1, 345--355.