How many times has Notre Dame played Ole Miss?

As of 2009, Notre Dame and Ole Miss have played twice, in 1977 and in 1985. The first game was won by Ole Miss, 20-13 (the only game that Notre Dame lost that season), and the second was won by Notre Dame, 37-14.

Source: http://www.olemisssports.com//pdf5/638465.pdf?&DB_OEM_ID=2600