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 __________.

Step-by-step solution

If group C has one student then number of groups C 1 10 2 9 - 2 = 5100 If group C has two students then number of groups C 2 10 2 8 - 2 = 11430 If group C has three students then number of groups = C 3 10 × 2 7 - 2 = 15120 So total groups = 31650