Aclass has 32 students. in how many different ways can five students form a group for an activity? (assume the order of the students is not important.)

This is a combination problem (35C5)
In general, it is the number of arrangements of 5 out of 35 (35P5) divided by the number of arrangements of 5 out of 5 (5P5), which reduces to 
35P5/5P5 = 35!/((30-5)!)  /  (5!/(5-5)!) = 35!/(5!(30-5)!) = 35C5.

Substituting values
35C5 = 35!/(5!30!)=35*34*33*32*31/(1*2*3*4*5) = 324632 ways