Question 599323
C(n,r) = (n!)/(r!(n-r)!)


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!)


C(17,7) = (17*16*15*14*13*12*11)/(7!)


C(17,7) = (17*16*15*14*13*12*11)/(7*6*5*4*3*2*1)


C(17,7) = (98017920)/(5040)


C(17,7) = 19448


So there are <font color="red">19,448</font> different groups.