From a class of 25 students, 10 are to be chosen for an excursion party. There are three students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen? 

Total number of students = 25
The number of students to go for excursion = 10
Options are:
All 3 of them join the party and 7 others join the party from remaining 22 students.
          Number of selections =                                   ...(i)
All there do not join the party and 10 join the party from remaining 22 students.
           Number of selections =                  ...(ii)
Hence, the total number of ways of selecting 10 out of 25 for an excursion party
                                             = 
                                             = 170544 + 646646 = 817190.