The students S _ 1 , S _ 2 , , S _ 10 are to be divided into 3...

If group $C$ has one student then number of groups

$C1 10 \left[{2}^{9} - 2\right] = 5100$

If group $C$ has two students then number of groups

$C2 10 \left[{2}^{8} - 2\right] = 11430$

If group $C$ has three students then number of groups

$= C3 10 \times \left[{2}^{7} - 2\right] = 15120$

So total groups$= 31650$