How do you cast an object to a Tuple?

Don't forget the () when you cast:

Tuple<string, string> selectedTuple = 
                  (Tuple<string, string>)comboBox1.SelectedItem;

As of C# 7 you can cast very simply:

var persons = new List<object>{ ("FirstName", "LastName") };
var person = ((string firstName, string lastName)) persons[0];

// The variable person is of tuple type (string, string)

Note that both parenthesis are necessary. The first (from inside out) are there because of the tuple type and the second because of an explicit conversion.

Your syntax is wrong. It should be:

Tuple<string, string> selectedTuple = (Tuple<string, string>)comboBox1.SelectedItem;

Alternatively:

var selectedTuple = (Tuple<string, string>)comboBox1.SelectedItem;