The answer is 19,448 different groups, using the formula from permutation and combinations C (n, r) = (n!) / (r! (n-r)!) which calculates the number of times where r objects can be chosen from n object.
So,
C (17,7) = (17!) / (7! *(17-7)!)
C (17,7) = (17!) / (7! *10!)
C (17,7) = (17*16*15*14*13*12*11*10!) / (7! *10!) then eliminate 10!
C (17,7) = (17*16*15*14*13*12*11) / (7*6*5*4*3*2*1) = (98017920)(5040)
C (17,7) = 19,448 different groups
