The students S 1 , S 2 , … , S 10 are to be divided into 3 groups A ,   B and C such that each…

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

${}^{10}C_1\left[2^9-2\right]=5100$

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

${}^{10}C_2\left[2^8-2\right]=11430$

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

$={}^{10}C_3\times \left[2^7-2\right]=15120$

So total groups$=31650$