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

Answers (1)

 

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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