Number of ways in which 7 persons can speak in 7 places such that order of three particular persons A,B,C is fixed = 7!3!=840.
ALTERNATE SOLUTION:
Selection 3 places from 7 places can be done =7C3ways.
No of ways in which three particular persons A,B,C can speak in this function =7C3(as order is fixed)
Now, remaining 4 people can speak in 4 places in 4! ways
∴ Required number of ways =7C3×4!=840