Question: In what county is the college that Joseph Hamilton served as the forth head football coach located?

Context paragraphs:
Ithaca, New York: Ithaca is a city in the Southern Tier-Finger Lakes region of New York.  It is the seat of Tompkins County, as well as the largest community in the Ithaca-Tompkins County metropolitan area.  This area contains the municipalities of the Town of Ithaca, the village of Cayuga Heights, and other towns and villages in Tompkins County.  The city of Ithaca is located on the southern shore of Cayuga Lake, in Central New York.  It is named for the Greek island of Ithaca.

Tom Keele: Tom Keele (born c. 1933) is a former American football coach.  He served as the head football coach at California State University, Northridge from 1979 to 1985, compiling a record of 31–42–1.  Keele graduated from Jefferson High School in Portland Oregon in 1951.  He attended the University of Oregon, where he played football for the Oregon Webfoots as a tackle from 1957 to 1959.  Keele began his coaching career in 1960 at North Eugene High School in Eugene, Oregon, working two years as an assistant football coach and sophomore basketball coach.  He moved to Oregon City High School in Oregon City, Oregon in 1962, serving as head football coach and leading his team to a 9–1–1 record.  The following year, he was hired as head football coach at the newly-formed Sheldon High School in Eugene.

Steve Stetson: Stephen "Steve" Stetson (born January 24, 1951) is an American golf coach and former football player and coach.  He is the current head men's and women's golf coach at Hamilton College in Clinton, New York.  Stetson served as the head football coach at Hamilton from 1982 to 1984 and again from 2006 to 2011.  He was also the head football coach at Boston University from 1985 to 1987 and Hartwick College from 1992 to 2001, compiling a career college football coaching record of 89–111–2.  Stetson was an assistant football coach at the University of New Hampshire from 2002 to 2005.

Ernest T. Jones: Ernest T. Jones (born January 18, 1970) is the current head coach at ASA Miami, a two-year college starting its first football season in 2015.  He was briefly running backs coach for the University of Connecticut Huskies football team.  He was head football coach at Alcorn State University.  He was named the head football coach after the 2007 season and served as head coach in 2008.  He was controversially fired from this position in December 2008.  He returned to the University of Cincinnati as the Director of Player Services in 2009.  For the 2010 he will be an assistant coach at the University at Buffalo under former University of Cincinnati assistant coach and now UB head football Coach Jeff Quinn.

June Jones: June Sheldon Jones III (born February 19, 1953) is an American football coach and former player, currently serving as a head coach of the Hamilton Tiger-Cats of the Canadian Football League (CFL).  He was the head football coach at Southern Methodist University (SMU), where he served as head coach from 2008 to 2014, before resigning on September 8, 2014.  Jones was also the head football coach at the University of Hawaii at Manoa from 1999 to 2007.  Previously, he coached in the National Football League (NFL): a three-year tenure as head coach of the Atlanta Falcons from 1994 to 1996 and a ten-game stint as interim head coach of the San Diego Chargers in 1998.

Willie Fritz: Willie Fritz (born April 2, 1960) is an American football coach and former player.  He is the current head coach at Tulane University.  From 2014 to 2015, he was head coach at Georgia Southern University.  From 2010 to 2013, he was the head football coach at Sam Houston State University.  From 1997 to 2009, Fritz served as the head football coach at the University of Central Missouri.  From 1993 to 1996, he was the head football coach at Blinn College, a junior college in Brenham, Texas.

Ted Karras Jr.: Theodore George "Ted" Karras Jr. (born December 10, 1964) is an American football coach and former player.  He was most recently head football coach at Walsh University, a position he held from December 2012 to November 2016.  Previously, Karras served as the first head football coach at Marian University in Indianapolis, Indiana.  He held that position from the program's inception in 2007 through the 2012 season in which Marian won the NAIA Football National Championship.  Karras played college football as a defensive tackle at Northwestern University from 1983 to 1986 and for one year (1987) in the National Football League (NFL) with the Washington Redskins.  From 2003 to 2005, he served as the head football coach at Rose-Hulman Institute of Technology.  His father, Ted Karras Sr., played for the Chicago Bears in the 1960s.  His uncles also played in the NFL: Alex Karras for the Detroit Lions and Lou Karras for the Washington Redskins.

Mark Raymond: Mark Raymond is an American football coach, currently serving as the head football coach at Williams College.  Raymond served as the head football coach at St. Lawrence University from 2010 to 2015, winning two conference titles and compiling an overall record of 31–30.  Raymond was named Liberty League Coach of the Year following the conclusion of both the 2010 and 2015 seasons at St. Lawrence.  Raymond was named head football coach at Williams College on February 24, 2016.

Joseph Hamilton (American football coach): Joseph L. Hamilton was an American football coach.  Hamilton was the fourth head football coach at Ithaca College located in Ithaca, New York.  He held that position for five seasons, from 1951 until 1955.  His coaching record at Ithaca was 7–22–3.  He currently serves as an emeritus professor at Ithaca.

Mike Kelly (gridiron football): Mike Kelly (born February 11, 1958) is an American gridiron football coach and former player, scout, and executive.  He is currently the head football coach at Widener University in Chester, Pennsylvania, a position he has held since 2014.  Kelly served as the head football coach at Valdosta State University from 1997 to 1999.  In 2009, he was the head coach and general manager for the Winnipeg Blue Bombers of the Canadian Football League (CFL).  He has served as an assistant coach at the high school football level, for several college football teams, and for professional teams in the CFL, XFL, and the National Football League (NFL).  Kelly played college football as a quarterback at Bluffton College—now Bluffton University—in the late 1970s.

Supporting paragraphs: Joseph Hamilton (American football coach) Ithaca, New York
Answer: Tompkins County