Find the number of different ways that an instructor can choose 7 students from a class of 35 students for a field trip.

Answer 1

The word "choose" is usually a good indicator that your are dealing with combinations rather than permutations, that is, the order in which the students are selected does not matter, so
35 choose 7 or C(35,7) or 35!/(7!28!) or 6,724,520

Answer 2

Find the number of different ways that an instructor can choose 4 students from a class of 19 students for a field trip. Hint: The order of selection of the students for the trip does not matter.

Answer 3

Find the number of different ways that an instructor can choose 7 students from a class of 21 students for a field trip.