The office of Administrative Assistant to the Supreme Court was created in 1972.
How long did Mark Cannon serve as Chief Justice Berger's Administrative Assistant?

Dear dave9,

Mark W. Cannon was Administrative Assistant to the Chief Justice of
the United States for 13 years from 1972, when the office was created,
to 1986, when William H. Rehnquist replaced Warren E. Burger as Chief
Justice.

Sources:

Meridian: How a Virginia Stake Awakened its Member-Missionary Work, by
Mark W. Cannon, 2002
http://www.meridianmagazine.com/missionaryjournal/020607virginia.html

The Supreme Court Historical Society: Society Publications
http://www.supremecourthistory.org/04_library/subs_volumes/04_c15_k.html

Institute of Public Administration: Trustees and Corporate Officers,
September 2002
http://www.theipa.org/aboutipa/boardbios.html

Search terms used:
"Mark Cannon" "Administrative Assistant":
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"Mark Cannon" burger "Administrative Assistant":
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"mark w cannon" "Administrative Assistant":
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"Chief Justices" "us supreme court":
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Hope this answers your question!
Regards,
Scriptor

Exactly the answer that I was looking for.   Many, many, many thanks.