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Three students can be selected from 5 in (5 x 4 x 3) = 60 ways.BUT there are (3 x 2) = 6 ways to select the same 3 students.So there are only 60/6 = 10 different groups of 3 studentsthat can be selected from a pool of 5.
if order does not matter then, (23x22x21x20x19)/(5x4x3x2x1) = 33,649
20 x 19 x 18/3 x 2 = 1,140 groups
Two groups of five is ten
There are only two possibilities... 10 groups of 2 or 5 groups of 4. Unless - you can have varying sized groups - which you didn't specify.