# The students $S_{1}, S_{2},.......,S_{10}$ are to be divided into 3 groups A, B and C such that each group has at least one student and the group C has at most 3 students. Then the total number of possibilities of forming such groups is _______. Option: 1 31650 Option: 2 3165 Option: 3 36150 Option: 4 3165

If group C has one student then number of groups

${ }^{10} \mathrm{C}_{1}\left[2^{9}-2\right]=5100$

If group C has two students then number of groups

${ }^{10} \mathrm{C}_{2}\left[2^{8}-2\right]=11430$

If group C has three students then number of groups

$={ }^{10} \mathrm{C}_{3} \times\left[2^{7}-2\right]=15120$

So total groups =31650

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