The American Symphony League criterion for "major symphony" yields a list of
about 27 organizations in the US.  If each of these 27 had a section of six
horns, there are 162 positions in the US.

There are other positions that would be similar to a major symphone - studio
work in Los Angeles for example.  Make a guess the total in the US is 250
give or take.

There are probably that many people graduating from schools with music
degrees across the US.

I thing you could play around with the numbers and show that the chances are
that there are good horn players that don't have gig's with a major
symphony.  Not great ones, but good ones.

With such a small number of positions, my guess is that there are lots of
pretty darn good horn players that don't have jobs with major symphonies.
Might even had decided that they didn't want to wait for an opportunity to
audition and have gone on to other careers.
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