Question

There are 25 students that would like to go on a field trip, but only 18 may go. How many different combinations of students could go on the trip.

Answer 1

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 $nC_{r}=\frac{n!}{r!(n-r)!}$. 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:

$25C_{18}=\frac{25!}{18!(7!)}=480700$