480700. The different combinations of students that could go on the trip with a total of 25 student, but only 18 may go, is 480700.
The key to solve this problem is using the combination formula [tex]nC_{r}=\frac{n!}{r!(n-r)!}[/tex]. This mean the number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.
The total of students is n and the only that 18 students may go is r:
[tex]25C_{18}=\frac{25!}{18!(7!)}=480700[/tex]
