Answer:
There are 5040 different ways to schedule their appearances.
Explanation:
Let A,B,C,D,E,F,G be the slots in which the given performs 1,2,3,4,5,6,7 can perform
For A we have 7 choices to select among(1,2,3,4,5,6,7 )
For B we have 6 choices to select among (2,3,4,5,6,7)
For C we have 5 choices to select among (3,4,5,6,7 )
For D we have 4 choices to select among (4,5,6,7 )
For E we have 3 choices to select among (5,6,7 )
For F we have 2 choices to select among (6,7 )
For G we have 1 choice to select (7)
Thus total different choices are 7!=5040
